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RATIONAL PHILOSOPHY 



THE LAWS OF THOUGHT 



FORMAL LOGIC 



A BRIEF, COMPREHENSIVE TREATISE ON THE 

LAWS AND METHODS OF CORRECT 

THINKING 



BY 



WILLIAM POLAND 
Professor of Rational Philosophy in St. Louis University 







SILVER, BURDETT & CO., PUBLISHERS 

New York BOSTON Chicago 

1892 






Copyright, 1892, 
By silver, BURDETT & CO. 



Typography by J. S. Gushing & Co., Boston. 



Presswork by Berwick & Smith, Boston. 



PREFACE. 



It may not be unwise to preface the following pages 
with a caution regarding their scope and purpose. Such 
caution may, indeed, be due not only to the writer lest 
his aim be misunderstood ; but also to the reader, who 
might otherwise seek in this little book for what it does 
not contain. 

This book, then, is not a Psychology. It does not 
discuss the nature of the soul or of its faculties. It 
merely enumerates the principal acts of the intellect ; 
and describes them as far as is necessary for the pur- 
pose of this book, which is to lay down briefly and 
clearly the process of right thinking. This requires no 
encroachment upon the field of psychology. 

Questions which should be discussed later on, in the 
course of philosophical studies, if introduced into an 
outline of correct thinking, only retard progress : firstly, 
because they are distracting; but especially because 
the mind is not prepared for them. Even after long 
discussions they are not understood by one who is just 
entering on the study of philosophy. 

Many things have been here omitted which would 
find a fitting place in an exhaustive treatise on Logic. 

3 



4 ' PREFACE. 

But they are such things as are not necessary to the 
purpose of this compendious work. Just as there are 
many curious combinations of numbers which might be 
introduced, and sometimes are introduced, into an arith- 
metic, but which are of no essential service in forming 
an accurate and rapid accountant ; so there are many 
things — curiosities — which may be introduced into a 
Logic, but which are in nowise necessary to prepare 
the mind for accurate and ready thought in the study 
of philosophy. 

On the other hand, this book is not intended as a 
sort of a ^^ Logic made easy,^^ or " Logic in twenty lessons 
without a master^ In philosophy less than in other 
things can we profitably dispense with a master. 

Finally, attention is called to the fact that terminology 
is strictly adhered to, both for the sake of brevity, and 
for ' the sake of the learner's progress, that he may 
be obliged to understand each section before passing 
further. 



CONTENTS. 



CHAPTER I. INTRODUCTORY. 

PAGE 

Article I. Logic. 

I. Logic. 2. Formal and Material Logic. 3. Natural Logic. 

4. Artificial Logic. 5. Logic as a Science. 6. As an Art . 9 

Article II. Three Acts of the Mind. 

7. Three Acts. 8. Knowledge Representative. 9. Simple 
Apprehension, Idea. 10. Judgment. 1 1 . Reasoning, Argu- 
ment. 12. Oral Expression. 13. Term. 14. Proposition. 
15. Syllogism 11 

CHAPTER II. IDEAS — TERiMS. 

Article I. Ways of Classifying our Ideas. 

17. Abstract, Concrete. 18. Clear, Distinct, Complete, 
Comprehensive. 19. Singular, Particular, Collective, Uni- 
versal 15 

Article II. Classification of Universal Ideas. 

20. Form. 21. Reflex Universal. 22. Species. 23. Impor- 
tant Observation. 24. Genus. 25. Difterence. 26. Prop- 
erty. 27. Accident. 28. Heads of Predicables .... 17 

Article III. Subordination of Genera. 

29. The Same Form Generic and Specific. 30. Diagram. 

31. Highest Genus, Lowest Species, Subaltern Genera . . 22 

Article IV. Classification and Use of Terms. 

32. Real and Logical Terms. 33. Univocal, Equivocal, 
Analogous Terms. 34. Univocal. 35. Equivocal. 36. Anal- 
ogous. 37. Supposition or Use ; Material, Logical, Real . 23 

5 



CONTENTS. 



CHAPTER III. JUDGMENTS AND PROPOSITIONS. 



PAGE 



Article I. Definitions. Structure of Propositions. 

38. Judgment. 39. Proposition. 40. Subject, Copula, 
Predicate. 41 . Logical and Grammatical Predicate ... 27 

Article II. Simple and Compound Propositions. 

42. Simple. 43. Compound. 44. Various Constructions. 
45. Categorical. 46. Conditional. 47. Conjunctive. 48. Dis- 
junctive. 49. Remark 28 

Article III. Immediate and Mediate Judgments. 

50. All Judgments. 51. Immediate. 52. Mediate. 53. The 
Process 31 

Article IV. Connection between Subject and Predicate. 

54. All Judgments. 55. A Priori. 56. A Posteriori. 57. No 
Synthetic a Priori 32 

Article V. Extension and Comprehension. 

58. An Axiom. 59. Extension. 60. Comprehension, 61. Il- 
lustration 34 

Article VI. Extension of Propositions. Quantity and Quality. 

62. Extension. 63. The Subject. 64. Note. 65. The Pred- 
icate. 66. Universal Affirmative. 67. One Exception. 
68. Universal Negative. 69. Particular Affirmative. 70. Par- 
ticular Negative. 71. Two Laws. 72. Affirmative and Neg- 
ative. 73. Negative Particle. 74. Quantity and Quality . 36- 

Article VII. Related Propositions. 

75. Three Relationships. ']^. Conversion, tj. Equiva- 
lence. 78. Opposition. 79. Diagram 41 



CHAPTER IV. REASONING — ARGUMENT. 

Article I. The Syllogism. 

80. Reasoning and Argument. 81. Styles of Argument. 
82. The Syllogism. 83. Antecedent, Consequent, Prem- 



CONTENTS. 7 

PAGE 

isses. 84. Consequence. 85. Axioms. 86. Analysis of 
Argument. 87. Middle and Extremes 45 

Article II. Figures and Moods of the Syllogism. 

88. Major, Minor, Middle. 89. First Figiu'e. 90. Second 
Figure. 91. Third Figure. 92. Moods of the Syllogism . 48 

Article III. Laws of the Syllogism. 

93. Scope of the Laws. 94. First Law: Three Terms. 
95. Second Law: Extension of Extremes. 96. Third Law: 
Extension of Middle Term. 97. Fourth Law : Place of 
Middle Term. 98. Fifth Law: Affirmative Conclusion. 
99. Sixth Law : Negative Conclusion. 100. Seventh Law : 
No Conclusion. loi. Eighth Law: No Conclusion. 
102. Ninth Law: Particular Conclusion. 103. Caution . 54 

Article IV. Some Species of the Syllogism. 

104. Simple and Compound Syllogisms. 105. Conditional 
Syllogisms. 106. Conjunctive Syllogisms. 107. Disjunc- 
tive Syllogisms 61 

Article V. Other Styles of Argument. 

108. Argument Abbreviated. 109. Enthymeme. no. Sori- 
tes. II I. Polysyllogism. 112. Epichirem. 113. Dilemma 64 



CHAPTER V. TRUTH OF THE PREMISSES. 

Article I. Formal and Material Logic. 

114. The Form. 115. The Matter. 116. Value of the 
Conclusion 68 

Article II. The Demonstration. 

117. Two Kinds. 118. Direct. 119. Indirect. 120. Sim- 
ple, Compound. 121. A Priori. 122. A Posteriori ... 70 

Article III. Induction. 

123. Deduction and Induction. 124. Complete Induction. 
125. Incomplete Induction. 126. Example. 127. Analogy. 
128. Caution 72 



5 CONTENTS. 

PAGE 

Article IV. Fallacies. 

129. Fallacy. 130. Petitio Principii. 131. Evading the 
Question. 132. Of the Accident. 133. A Dicto Simpliciter. 
134. Of the Consequent. 135. Of the Cause. 136. Of the 
Question. 137. Of Reference. 138. Of Objections . . . yj 

CHAPTER VI. METHOD. 

Article I. Scientific Method. 

139. Scientific Method. 140. Analysis and Synthesis . . 82 

Article II. Definition. 

141. Definition. 142. Nominal Definition. 143. Real Defi- 
nition. 144. Rules for Definition 83 

Article III. Division. 

145. Scientific Division. 146. Physical and Metaphysical 
Parts. 147. Actual Union. 148. Integral Parts. 149. Logi- 
cal Division. 150. Potential Parts. 151. Logical Whole. 
152. Importance. 153. How to Divide -87 

Article IV. Analysis and Synthesis. 

154. The Question. 155. The Answer : Analysis, Synthe- 
sis. 156. Analysis. 157. Synthesis. 158. Explanation 
Complete. 159. Singular to Universal, and vice versa. 
160. Complex to Simple, and vice versa. 161. Discovery 
and Instruction. 162. Analytic and Synthetic Sciences. 

163. Advice 91 

Article V. Science. 

164. Science. 165. Object of a Science. 166. Material and 
Formal Object. 167. A Delusion. 168. Outline of the 
Sciences. Explanation of Outline 96 

Points for Practice 100 

Index loi 



THE LAWS OF THOUGHT. 



oJOio 



CHAPTER I. INTRODUCTORY. 

Article I. Logic. 
Logic — Formal and Material Logic — Natural and Artificial Logic. 

1. The name Logic comes from the Greek, X0709. 
A0709 signifies reaso7i, thought; also oral speech, a word. 
But the oral word, oral speech, is merely a sign of what 
is in the mind, of the mental word, mental speech, 
thought. Logic, therefore, has to do with thought. 

2. Formal Logic is so called in opposition to Material 
Logic, because it deals solely with the form or structure 
of thought, of an argument ; and not with the matter 
contained in the structure. In the building of a house 
there are different persons or sets of persons concerned. 
Besides the architect there are those who supply and 
prepare the material, and there are the builders. It is 
the business of the architect to see that the material 
is supplied and properly prepared by one set and put 
together by the other. The builders have not to 
question the nature, value or strength of the material. 
They have only to see that the pieces fit. They 
are concerned only with the shape, the fonn of the 



10 THE LAWS OF THOUGHT. 

structure and of each piece as tending thereto. Now, 
apply this to the edifice of knowledge. Formal logic 
has to do with the principles for the correct putting 
together of the material furnished. The general method 
of furnishing the material ready prepared is the sub- 
ject of material logic. Hence in formal logic we have 
to work at, to study, only the q,oxxq.qX. form of thought; 
not minding whether the examples we take to practice 
upon be true or not: just as one wishing to illustrate 
the structure of a bridge will take bits of wood, paper, 
straw, thread, wire or whatever he may find at hand, 
occupied solely, for the moment, with the form; and 
not at all concerned about the material. 

3. Natural Logic. Natural logic is the innate dispo- 
sition all men have to think correctly, to follow certain 
rules in the pursuit of knowledge, of truth. We are all, 
by nature, logicians. 

4. Artificial Logic. However, as sometimes, even with 
the best intentions, we are liable to think inaccurately 
by reason of complications of notions which arise and 
defects which are easily overlooked in the process of 
our thought, there has been invented what is called an 
artificial logic. Not that there is anything artificial about 
it in the sense that it is intended to replace real logic ; 
but, in this sense, that it is made an art whose princi- 
ples we can learn and apply, to ensure correct thinking. 
The methods which we follow when we think correctly 
have been closely observed and have been put together 
as a connected system of rules. By learning to apply 
them we can acquire the art of logic. 

5. Logic as a Science. But logic is not merely an art. 
It is primarily a science. For these rules are a system- 



INTRODUCTORY. ll 

atized body of fixed laws regarding the reason of cor- 
rectness in thought. Hence logic as a science may be 
defined : " The science of those laws which must rule 
the acts of the mind in correct thinking." 

6. Logic as an Art. Logic becomes an art when these 
laws are presented, or made ready instruments, for use, 
to ensure right thinking, to detect false reasoning, and 
to mend faulty argument. 



Article II. Three Acts of the Mind. 

Simple Apprehension ; Judgment ; Reasoning — Idea ; Judgment ; 
Argument — Term ; Proposition ; Syllogism. 

7. Three Acts of the Mind. To find out the rules which 
we must follow in aiming at a knowledge of truth, we 
must consider three acts which the mind performs in 
obtaining knowledge. They are : i. Simple Apprehen- 
sion ; 2. Judgment; 3. Reasoning. 

8. Knowledge Representative. All knowledge is repre- 
sentative of something real or possible. It is a mental 
expression of that something. Hence every act of the 
mind by which we know may be considered in two 
ways : either with reference to the degree of activity 
called forth or with reference to the degree in which it 
is representative. 

9. Simple Apprehension. Simple apprehension is an 
act by which the mind simply perceives or apprehends 
something without affirming or denying anything about 
it. If we consider this act as representative, as a mental 
expression of that something, it is called an idea (like- 



12 THE LAWS OF THOUGHT. 

ness), a concept (the mind conceiving that something in 
itself, in likeness), a notion (the first element of knowl- 
edge). Thus by the act of simple apprehension we may 
have a notion, an idea, a concept, of rose, blue, plant, 
cloth, beauty, justice, etc. 

Remark that when we perceive or apprehend we do 
not perceive the idea, but the object which the idea 
represents. We do not advert, at least not especially, to 
the act of the mind. It is only by a second act of the 
mind, called reflection, that we perceive we are per- 
ceiving. 

10. Judgment. Judgment is that act by which the 
mind, having formed two ideas, ai^rms or denies identity 
between their objects. Thus : TJie rose is a plant, This 
cloth is not blue. Remark, as for the simple apprehen- 
sion, that what we affirm or deny is not about the ideas, 
but about the objects which the ideas represent. This 
is expressed by saying that we affirm or deny objective 
identity. The judgment, as the simple apprehension, 
may be regarded as a certain exercise of the activity of 
the mind, or as representative of the presence or absence 
of objective identity. As an act it is called judgment; 
as representative it is also called a judgment or a 
declaration. , 

11. Reasoning. Reasoning is aji act or a series of acts 
by which the mind compares (objectively) two cases pro- 
nounced upon in two judgments, and in that compari- 
son perceiving implied the material for a third judgment, 
thereupon forms explicitly such third judgment affirming 
or denying according to what was perceived implicitly 
through the comparison. This definition will be made 
sufficiently clear for present purposes by two examples : 



INTRODUCTORY. I3 

First example. The judgment makes two declarations : 

A man is a living being; 
Hannibal is a man. 

The mind compares these two cases and then declares 
explicitly what it perceives implied, namely: 

Hannibal is a living being. 

Second example. The judgment makes two declara- 

^*^" ■ A horse is a quadriiped; 

This feathered being is not a quadruped. 

The mind compares these two cases and then declares 
explicitly what it perceives implied, namely : 

This feathered being is not a horse. 

In the first example the mind worked upon the prin- 
ciple that, in the sense in which two things {^living being, 
Hannibal) are the same as a third thing {man), in the 
same sense are they the same as one another. In the 
second example the mind worked upon the principle that, 
in the sense in which two things {horse, this feathered 
being ) are, the one (horse) the same as ^ third thing 
{quadruped), the other {this featJiered being) different 
from it, in the same sense are they different from one 
another. 

As in the simple apprehension and judgment the 
action of the mind was also regarded as representative, 
so the act of reasoning may be regarded as carrying in 
its third judgment a new representation of something 
perceived through the two prior judgments. Considered 
as an act it is called reasoning, argumentation, deduction. 
In the other sense it is called argument, and also some- 
times inference, conclusion. 



14 THE LAWS OF THOUGHT. 

12. Oral Expression of Thought. Just as our thoughts 
are, as it were, mental words expressing certain objects, 
so in written and spoken words do we express our 
thoughts as well as the objects represented in our 
thought. 

13. Term. The oral (spoken) or written word express- 
ing an idea is called a term, as, bhte, cloth, j^istice, beauty. 

14. Proposition. The terms, oral or written words, 
expressing a judgment are called a proposition, as, 
Hannibal is a man. 

15. Syllogism. The three propositions expressing an 
argument are called a syllogism, and also an argument. 



CHAPTER II. IDEAS, TERMS. 

16. We shall now proceed, within the limits of the 
scope of Formal Logic, to make some considerations 
upon ideas, judgments, arguments ; and upon their 
respective verbal expressions, terms, propositions, syllo- 
gisms. We begin with the most elementary, the idea. 



Article I. Ways of Classifying our Ideas. 

17. There are many ways of partitioning off into 
classes all the ideas we have or may have. 

I. Abstract and Concrete. An abstract idea is one 
which represents its object as independent of, taken 
asunder from {abstracted from), everything else. A con- 
crete idea represents its object as coalescing with, in 
union with, grown together with {concreted) something 
else. Our ideas of blueness, wisdom, are abstract. Our 
ideas of blue, zvise, are concrete, because bine, wise, are 
thought of as concreted in something else : blice sky, wise 
judge. 

18. 2. Clear, Distinct, Complete and Adequate or Compre- 
hensive. According to the degree of perfection with 
which ideas express the characteristics (called notes) of 
their object, they are divided into clear, distinct, complete 
and adequate or comprehensive. 

A clear idea expresses characteristics or notes suf- 
ficient to discern the object from others. A distinct 



l6 THE LAWS OF THOUGHT. 

idea distinguishes between these notes themselves. A 
complete idea expresses all the notes that distinguish the 
object /;/ reality from others. A comprehensive or 
adequate idea expresses all that can be perceived in the 
object : the human intellect has no such idea of any- 
thing. 

I see an object moving in the distance. I have 
an indefinite, obscure idea of something moving. It 
approaches. I get an idea of my friend X — just 
enough to know that it is X without distinguishing any 
marks — a clear idea. X comes nearer. Yes, there is 
the walk and build and countenance of X. My idea is 
becoming, distinct. X steps up and shakes hands with 
me. I know X intimately and thoroughly. I note all 
the points that distinguish him as X from aught else. 
My idea is complete. 

19. 3. Singular, Particular, Collective, Universal. Ideas 
may again be divided according to the number of indi- 
viduals embraced in the idea and the manner of embrac- 
ing them ; that is, according to the extension of the 
idea. In this way we divide ideas into singular, par- 
ticular, collective, universal. 

When one special individual is expressed in a deter- 
minate manner, we have a singular idea. Thus : Canada, 
" The President,'' to-day, this book. 

When the idea expresses in an indeterminate way 
some one or other individual or some individuals, it is 
called particular. Thus : Some man or other, a man, a 
certain man, some men. 

When several objects are expressed under one idea 
or concept, but in such a way that the idea cannot be 
applied to them individually but only as a collection, the 



IDEAS, TERMS. 1/ 

idea is called collective. Thus : A cjvivd, a fleet. No 
individual of the collection is a crowd or a fleet. 

When several objects are expressed by an idea, but in 
such a way that the idea not only embraces them all, 
but is applied to them distributively and individually, 
we have what is called a universal idea. Thus : Ma7i, 
horse, gold. I can say, Man is a living being, mean- 
ing that all men are living beings ; meaning also that 
each individual man is a living being. When I say. The 
horse is a quadruped, I mean that all are quadrupeds, 
and tJiis horse is a quadruped. When I say. Gold is a 
metal, I mean that all gold and that this piece of gold 
is metal. 

This partition of ideas being made, we have to deal 
now, in a special manner, with universal ideas. 



Article II. Classification of Universal Ideas. 

Species — Genus — Difference — Property — Accident. 
Heads of Predicables. 

20. Form. Universal ideas are classified according to 
the manner in which the one idea can be applied to 
many individuals ; or, what comes to the same, accord- 
ing to the manner in which what the idea represents 
belongs to many individuals. This will explain itself as 
we proceed. Let us for the purpose of clearness and 
brevity introduce a new word, form or formality. We 
shall call form or formality whatever can be the object 
of an idea. The same thing may have r(\2iny forms (or 
determinations) existing in it simultaneously. A ball 
may contain the forms of wood, roundness, whiteness, 



1 8 THE LAWS OF THOUGHT. 

elasticity, etc. In man there are the forms of spirit, 
matter, orgajtism, sensation, etc. 

21. Reflex Universal. Any form or formality may 
become the object of my idea. This idea I may reflect 
upon, and then regard as applicable not only to the 
individual form from which I first got it, but as appli- 
cable to an indefinite number of individual cases, actual 
or possible, and also as sufficiently representative of the 
same formality as it exists or may exist in each of those 
cases. I begin to regard the idea as universal, as 
applicable to many, by reflecting upon it. The idea, as 
so regarded by reflection, is called a reflex universal idea. 
Even before I reflected upon it, even as I got it directly 
from the individual /<?r/;z, it was in itself capable of being 
applied to the indefinite number of cases. As such, 
prior to reflection, it is called a direct universal. 

22. Species. If a form constitutes, or if combined 
forms constitute, the whole essence of a class of indi- 
viduals, so that no individual of the class can be, or 
be thought, without said form or combination, then such 
form or combination is said to be specific, and the reflex 
universal idea representing it is called a specific idea. 
Thus the combination of ratiotial and animal in man 
constitutes his essence. The complex idea rational 
animal regarded as applicable to all possible men is a 
specific idea. 

23. Important Observation. Now here we have some- 
thing curious to note. The idea rational animal is one 
idea — complex, but one. Where, when we apply it to 
all men actual and possible, has it one object } When 
we. speak of tJie rational animal^ of rational animals^ of 



IDEAS, TERMS. I9 

humanity, we find ourselves figurinjT; to ourselves a 
certain something outside of us which is neither this 
man nor that man nor the great collection of all men. 
Yet is it something which we do put up before us as the 
object of our universal reflex idea, rational aniuial, 
Jimnaiiity ; and we talk of it as if it were something, a 
man in general. We know that what we say of it is 
true of each case where there exists the rational animal, 
where there exists Junnanity. What is it .-' It is a con- 
venience invented by the ingenuity of the mind for the 
needs of thought. It is consequent upon the innate 
tendency of the mind to pursue the most profitable and 
expeditious modes of thought. It is something we 
create in possessing ourselves of the reflex universal 
idea. It is a something that does service for all the 
individual cases. We call it the species. I know that 
the expression Jinmaii species suggests to us the whole 
collection of men, and that naturalists do use the word 
species to express collections. But we do not reason upon 
collections. We should never get through. Neither do 
we reason, when speaking, for instance, of man, upon 
this man or that man. When we say man is mortal, we 
speak of man, in general, taken as a species, in the sense 
explained. 

24. Genus. If the form be something that is found in 
all the individuals of two or more classes so as to con- 
stitute /«r/ of the essence of such individuals, or briefly, 
if the form be found as part of the essence in two or 
7nore species, it is called generic, and the reflex universal 
idea representing it is called a generic idea. Thus man 
and brute agree in this, that they are both animal ; the 
formality animal is of the essence of the species man 



20 THE LAWS OF THOUGHT. 

and of the species bnite. Animal, therefore, is generic, 
and applies to all the individuals of the two species. If 
now we put before us that certain something which will 
stand as one for all the individuals possessing animal 
nature, we shall have what is called a genus. 

25. Difference. Now take two species. They agree 
in something that is common to the essences of both. 
This, as we have said, is genus. But they differ also in 
other essentials. All the individuals of one species have 
a formality which is not in any of the individuals of the 
other, and which distinguishes all the individuals of one 
from all those of the other. The reflex universal idea 
of this formality is called a differential idea ; and as this 
stands out objectively in the species, it is called a differ- 
ence or specific difference. Take the genus animal. It 
embraces the two species, rational animal and irrational 
animal. Rational and irrational are specific differences. 

26. Property or Inseparable Accident. Sometimes 
there is found a form in all the individuals of a species, 
which form, though not of their essence, is still neces- 
sarily connected with the essence and flows from it. 
The reflex universal idea of a form so considered is said 
to be the idea of a property. Such form, considered in 
the species, as we have explained species, is named a 
property or an inseparable accident. Such may be con- 
sidered, for instance, the powers of speech and of 
laughter in man. 

27. Accident. If, however, a certain form happen to 
be common to many individuals, but be in nowise of 
their essence nor necessarily connected therewith, and 
be such that it can be added or taken away without 



IDEAS, TERMS. 21 

affecting the essence, such form is said to be simply 
accidental. The universal reflex idea representing it as 
so separable is the idea of an accident. The form itself, 
in whatever way considered, as thus separable, is called 
an accident. Thus the forms, bliiCy green, circular, square, 
thick, soft, etc., are separable accidents. We distinguish 
the inseparable accidents by the special name of 
property. 

28. Heads of Predicables. The wide reaching nature 
of the classification which has just been given, will be 
seen if we consider that whatever we afifirm or deny of 
anything is affirmed or denied as a gejiiis, species, differ- 
ence, property or accident. That is to say, whatever 
we predicate (affirmatively or negatively) we predicate 
(affirmatively or negatively) as the genus, species, etc., of 
that of which we predicate it. Thus we say maji is a 
rational animal. We predicate rational animal of man. 
We predicate it as the species. If we say mail is rational, 
we predicate rational as the specific difference. If we 
say man is an animal, we predicate animal as the genus. 
If we say the man is ivhite, yellow, strong, we predicate 
white, yellozv, strong as accidental, as accidents. Hence 
genus, species, difference, property, accident, are called 
Heads of predicables, because whatever is predicable of 
anything comes under one of these heads. There is a 
single exception to this general law. The exception is 
for the form being. Being applies to whatever can 
exist or be thought of. The idea of being is said to be 
transcendental. But the predication of beijig (as also of 
07ie, true, good) constitutes one of the most subtle dis- 
cussions of general metaphysics. We need not speak 
of it here. 



22 THE LAWS OF THOUGHT. 

Article III. Subordination of Genera. 
Highest Genus — Subaltern Genera — Lowest Species — Individuals. 

29. The Same Form Generic and Specific. It is to be 

remarked that there are cases where the same form 
considered as a universal is capable of being regarded 
as both genus and species. Take, for instance, the form 
substance. Since the individuals to which it extends 
can be divided into the two classes, corporeal substance 
(body) and incorporeal substance (spirit), it is genus with 
reference to them, and they are species embraced by it. 
But the form corporeal substance (body) is again a genus 
when regarded as universal, for it extends to individuals 
that can again be divided into classes, — organic body and 
inorganic body. These become species under it. Or- 
ganic body, next taken as a universal, becomes 2i genus 
with reference to the classes sentient organic body (ani- 
mal) and non-sentient organic body (plant). These are 
species under it. But animal is also genus with refer- 
ence to rational animal and irrational animal. 

30. Diagram. The following plan will exhibit this to 
the eye : 

Substance. 

\ 



Corporeal Substance or Body. Incorporeal Substance. 



Organic Body. Inorganic Body. 



Sentient Organic Body or Animal. Non-sentient. 



Rational Animal or Man. Irrational. 

J 

[Charles, Frederic, Augustus, etc. | 



IDEAS, TERMS. 23 

31. Highest Genus, Lowest Species, Subaltern Genera. 

In this table it is seen that substance is used as genus 
only. Body, organic body and animal are used both 
as species and as genus. Maji is used as species only. 

When a genus cannot be considered as a species 
under a higher genus, it is called highest genus. 

When a species under one genus cannot be made a 
genus with reference to individuals under it, that is, 
when the individuals cannot be classified as species, it is 
called lowest species. 

The forms that are predicable both as genius and as 
species are called subaltern genera. 

In the table, Substance (supposing it to be incapable 
of being ranged as species under a higher genus) is 
highest genus. Man is loivest species. Body, Organic 
Body, Animal, are subaltern genera. Charles, Frederick, 
Augustus, etc., are merely individuals of the species 
man. 



Article IV. Classification and Use of Terms. 

Real, Logical — Univocal, Equivocal, Analogous — Supposition. 

32. Real and Logical Terms. We may now say a word 
about terms. Terms are the written or spoken words 
that stand for ideas or for the objects of ideas. A term 
is called real when it expresses an object as that object 
may exist independently of the mind. Thus London, 
this man, are real terms. A term is called logical when 
it expresses an object in that kind of existence which 
depends entirely on the mind, as man, animal, used in 
the universal sense to stand for genus or species, v. gr., 
for animal and man in general. Genus and species as we 



24 THE LAWS OF THOUGHT. 

have explained them are mental creations, doing service 
as representatives for a class, or what is the same, their 
existence is logical, dependent on the mind. Hence the 
terms expressing them as such are called logical terms. 

33. Univocal, Equivocal, Analogous Terms. Leaving 
the real terms and concerning ourselves solely with the 
logical, we find that, on account of the defects of 
language, some terms, doing service as universals, do 
not always represent the same ideas nor apply in the 
same manner to all the individuals for which we make 
them stand. We find terms to be not only univocal, 
but also equivocal and analogous. 

34. Univocal. That term is called univocal (one word) 
which is really but one term in meaning as well as in 
sound. That is to say, the univocal term is always 
applied with the same signification to each and all of 
the inferiors {i.e. species or individuals) to which it can 
be applied. Such are the terms, animal, man. 

35. Equivocal. But if the same written or spoken 
word, the same term, comes, in the complexity of 
language-growth, to stand for two or more different 
ideas and objects of ideas, it is called an equivocal term. 
Thus the term pen is equivocal. It is a ivord that 
serves equally to express different ideas and objects of 
ideas. It stands equally for a zvriting instrument and a 
cattle enclosure. The equivocation is sometimes in the 
sound only, as boiv (a reverence) and bough. Sometimes 
it is in the writing only, as bovo {a reverence) and bow (in 
archery). 

36. Analogous. Again, there are terms that are ap- 
plied to different things neither univocally {i.e. in quite 



IDEAS, TERMS. 2$ 

the same meaning), nor cqiihwcally {i.e. in quite different 
meanings), strictly speaking. The same term is used 
on account of some connection between the objects. 
The connection is called, in philosophy, analogy. The 
terms are called analogous terms. 

When the analogy or connectiofi is merely a likeness 
between the objects, it is called analogy of proportion. 
We make this the ground for the use of the metaphor. 
We will call a man a lion on account of his courage. 
We merely abbreviate a comparison. 

There is another analogy where the connection is 
closer. We say a healthy man and also (however justly) 
a healthy climate, a healthy complexion. We affirm of 
the climate (which is the cause) and of the complexion 
(which is a natural sign) the attribute which, in its full, 
original and proper meaning, belongs only to the man. 
We have here again, strictly speaking, figures of speech. 
This analogy is closer than the mere similitude. It is 
called analogy of attribution. However, it is specified as 
analogy of extrinsic attribution, because the form that 
is attributed, health, is intrinsic to man only, belongs to 
man only, and is extrinsic to climate and to complexion, 
they being but the cause and the sign of man's health. 
But we have introduced this question only to come to 
what is called the analogy of intrinsic attribution. And 
we speak of the analogy of intrinsic attribution only as 
an aid to the understanding of a later question, the 
subtle question of the attribution of being, referred to 
in 28. Therefore — 

What is attributed may really exist in all the individu- 
als to which it is attributed, and still not in such a way 
that it can be attributed univocally, i.e. in the very 
game sense and manner. It exists in one independently 



26 THE LAWS OF THOUGHT. 

of all the others, but in the others only dependently 
upon this one. Thus being is predicated of God and 
of created things : of God, independently ; of created 
things, only with dependence upon the Creator. Being 
is not used nnivocally. It does not apply in the same 
sense to Creator and Creation. It cannot be called 
gemts. Under genus the species are independent one 
of another. But this question will be treated in the 
General Metaphysics. 

37. . Supposition. The supposition of a term is what is 
sub-posed by {put unde?) the term, what is implied by it 
or intended to be understood by it. This depends upon 
the wish of the one who uses the term. We might 
extend this subject and go back over all the various 
classifications of ideas and their corresponding objects. 
We shall give but three wide divisions of the supposi- 
tion and thus close this chapter. 

The supposition is said to be material when we imply 
no more than is evident from the mere sound of the 
term or its appearance as written. Thus, when we say 
or write, Man is a word of one syllable, our use or sup- 
position of the term man is material. 

If we imply that the term is used in the universal 
sense to stand for genus or species, the supposition is 
called logical. In the sentence, Man is a ratio7ial ani- 
mal, the supposition of the term man is logical. 

When we wish the term to stand for a reality, the 
supposition is called real. In the sentence. This man 
is temperate, the supposition of the term man is real. 



CHAPTER III. JUDGMENTS, PROPOSITIONS. 



Article I. Definition and Structure of 
Propositions. 

38. Judgment. Tho, Judgment, as we have said, is that 
act of the mind by which we compare two objects of 
thought and pronounce upon their identity or agree- 
ment, affirming or denying. It is an affirmation or a 
denial. 

It is not always necessary that any appreciable time 
should be taken to compare the terms before passing 
sentence. There may be and there are cases where 
the verdict is evident at once upon the presentation of 
the terms. We see at once the identity or the disagree- 
ment. Our daily thoughts are full of instances in 
point. 

39. Proposition. We have already stated that the 
judgment as expressed in spoken or written words is 
called a proposition. 

40. Subject, Copula, Predicate. A proposition consists 
of three parts, subject, copula, predicate. The subject is 
that of which something is affirmed or denied. The 
predicate is that which is affirmed or denied of the sub- 
ject. The copula is a word or words expressive of the 
affirmation or denial, the words, namely, is, are, is not, 
are not. 

27 



SUBJECT. 


COPULA. 


Man 


is 


Knowledge 


is not 


Vices 


are 


Sinners 


are not 



28 THE LAWS OF THOUGHT. 

PREDICATE. 

rational, 
virtue, 
detestable, 
saints. 

The copula is a convenience of language. It merely 
stands for the agreement or disagreement that exists in 
the objects ; this agreement or disagreement is perceived 
by the mind comparing the ideas, and is finally pro- 
nounced upon in the judgment. 

41. Logical and Grammatical Predicate. We must be 
careful to distinguish between the predicate of the 
logician and the predicate of the gramniaria7i. In the 
sentence, Birds fly, the grammarian may tell us that^ 
is the predicate. The logician will resolve the sentence 
in such a way as to employ the copula. He will say, 
Birds are beings-thatfly ; and with him the predicate is 
beings-thatfly. Thus the logician will transform any 
sentence to put it into logical shape. 



Article II. Simple and Compound Propositions. 

Simple — Compound — Copulative — Disjunctive — Conditional — 
Causal. 

42. A Simple Proposition contains but one principal 
subject and one principal predicate. The ship is sailing, 
is a simple proposition. We may add circumstances of 
time and place, adjectives, adverbial and relative clauses, 
without making it a compound proposition. It will 
become complex, but not compound. The ship that zvas 



JUDGMMSTTS, PROPOSITIONS. 29 

made last year at New York is sailing amid icebergs that 
have floated from Greenland to the coast of Neiufoundland, 
is still for the logician a simple sentence though complex. 
All that belongs to ship goes in as subject. All that 
belongs to sailing goes in as predicate. 

43. A Compound Proposition contains two or more 
principal subjects and predicates expressed or implied. 
Paris and Berlin are beautiful is a compound proposi- 
tion and stands for the two simple propositions Paris is 
beautiful, Berlin is beautiful. Add another predicate : 
Paris and Berlin are large and beautiful. Here we 
have four simple propositions in the compound. 

44. Various Constructions. There are various kinds 
of simple and compound propositions — various as the 
grammatical constructions invented to secure brevity in 
language, the sometimes cumbersome vehicle of thought. 
The propositions receive their names from the construc- 
tions. We call attention to a few propositions. 

45. Categorical. A categorical proposition is one that 
affirms or denies absolutely and directly. It may be 
simple or compound. Thus : Man is rational, The soul 
is not material, Prudence ajid Justice are virtues. Camels 
and giraffes are not insects. 

46. Conditional. A conditional proposition affirms or 
denies not absolutely, but on condition. The rain is 
comijtg is categorical. But, If the zvind is west, the rain 
is coming is a conditional proposition. Remark that 
this is really a simple proposition. We do not say, TJie 
ivind is west, the rain is coming. We merely affirm con- 
ditional connection between the two. The conditional 
proposition is also called hypothetical. 



30 THE LAWS OF THOUGHT. 

47. Conjunctive. A conjunctive proposition affirms 
the simultaneous incompatibility between two cases. 
No man can spend all his money on drink and still sup- 
port his family. Here we do not affirm or deny the 
categorical propositions that he spends his money on 
drink, that he supports his family. We affirm only the 
incompatibility between the two. The proposition is 
simple, however complicated in language. The conjunc- 
tive proposition is reducible to the conditional thus : If a 
man spends all his money on drink, he cannot support his 
family. The conjunctive proposition is therefore a 

species of the hypothetical. It is always negative. It 
is called conjunctive for the sake of a name, on account 
of the conjunctive particle and which connects the 
incompatible cases. 

48. Disjunctive. A disjunctive proposition is made 
up of two or more categorical propositions connected 
in such way by a disjunctive particle that no one is 
declared absolutely, but the acceptance of one implies 
the rejection of the others. Thus, speaking of a per- 
son's age, I may say, He is either Just fifty or under 
fifty or past fifty. Suppose I declare categorically that 
he is just fifty ; then the two other parts become he is 
not imder fifty, he is not past fifty. However, the denial 
of one case does not imply the affirmation of the other 
two. If I say. He is not just fifty, I may not therefore 
affirm both that he is under fifty and tJiat lie is past 
fifty. The remaining parts are simply left in the 
diminished disjunctive proposition. He is either under 
fifty or past fifty. The disjunctive proposition is a 
species of the hypothetical, with one part positive and 
the other part negative. Thus : If he is just fifty ^ he is 



JUDGMENTS, PROPOSITIONS. 3 I 

neither under fifty nor past fifty. As the example given 
implies two such conditions, we might class it with the 
compound propositions ; but this matters nothing to our 
purpose. 

49. Remark. Here we shall leave the complex and 
compound propositions. We have mentioned the con- 
ditional, conjunctive and disjunctive, because we shall 
have occasion to refer to them when treating of the 
varieties of the syllogism. 

Henceforth in the present chapter we shall confine 
our study to the elementary proposition, the simple cate- 
gorical proposition. 



Article HI. Immediate and Mediate Judgments. 

50. All Judgments. The judgments we form are all 
necessarily either immediate or mediate. 

51. Immediate. An immediate judgment is one that 
is formed without a process of reasoning. If some one 
says to me, A ivhole orange is greater than half ati orange, 
I do not ask him to prove it. I see the truth immedi- 
ately, and pronounce upon i; without having to be led 
to see it through the medium of other truths better 
known. Again, if I take a piece of heated iron in my 
hand, I can and do know and say at once, TJiis iron is 
hot. I do not have to go through any other judgment 
to arrive at the knowledge that this iron is hot. The 
judgment is immediate. 

52. Mediate. On the other hand, if some one tells me 
that the three angles of a triangle are equal to tivo right 
angles, I do not see at once that it is so ; I ask him to 



32 THE LAWS OF THOUGHT. 

show me that it is so. And he proceeds to put before 
me other propositions through which I see, until it dawns 
upon m.e that what he said at first is true. These other 
propositions or truths are the mediufn through which I 
see that the three angles are equal to two right angles. 
This judgment is therefore called a mediate judgment. 
To take another example. I hand a banknote to some 
one, as payment. He tells me, This banknote is a coini- 
terfeit. I do not perceive that the note is a counferfeit. 
He imparts to me some new knowledge, and through the 
medinm of that knowledge, I too can see and say, TJiis 
note is a counterfeit. My judgment is mediate. 

53. The Process. The process by which one judgment, 
proposition, is made evident through the medium of 
others is called reasoning. This will form the subject 
of the next chapter. We have still to consider, in this 
chapter, two other divisions of judgments or propositions. 
This we shall do in the two following articles. 



Article IV. Connection between Subject and 
Predicate. 

A Priori, A Posteriori — Necessary, Contingent — Absolute, H3rpo- 
thetical — Metaphysical, Physical — Analytical, Synthetical. 

54. All Judgments. If we consider the connection 
that exists between the predicate and the subject, we 
can classify all judgments as a priori or a posteriori. 

55. A Priori. If the predicate is such that it is always 
implied in the subject, and in such way that a full under- 
standing of what is meant by the subject and predicate 
is sufficient, without any experiment upon a particular 



JUDGMENTS, PROPOSITIONS. 33 

case, to make us see that the proposition holds in all 
cases, absolutely, necessarily and without possible excep- 
tion, the proposition or judgment is called a priori. It is 
seen to hold prior to any application to a particular case. 
A zvJiole is greater than any of its parts ; no tiling can 
sininltancoiisly exist and not exist, — these are a priori 
propositions. 

Such propositions are also called necessary, because 
an exception is impossible. They are called absolute, 
because they hold, absolved from, free from, all condi- 
tion. They are called victapJiysical, because their truth 
does not depend upon the physical, actual order of 
things existing. They are called analytical, because by 
analyzing the subject, by taking it asunder into all that 
it implies, we will linally arrive at the predicate and see 
that the predicate belongs to the subject. 

56. A Posteriori. An a posteriori proposition is one 
in which the idea of the predicate is not implied in the 
idea of the subject. Some one says to me, TJiis iron is 
hot. I may know all that books can teach about the 
nature of iron and the nature of heat. But all of it will 
not teach me that this iron is hot. I must have experi- 
ence of this particular case of iron and heat. After the 
test, posterior to the experience, I may affirm, TJiis iron 
is hot. Hence the name a posteriori. 

Such propositions are also called contingent, as opposed 
to necessary, because they may happen to be true or not 
true. They are called hypothetical, as opposed to abso- 
Inte, because their truth depends upon a supposition, a 
hypothesis, which may be wanting. They are called 
physical, because they represent facts of the actual, 
physical order. Finally, they are called synthetic, as 



34 - THE LAWS OF THOUGHT, 

opposed to analytic, because they are made up by the 
syntJiesis, the putting together, of two ideas, terms, 
neither of which is found in the analysis of the other. 

57. Synthetic a Priori. We have here to make a re- 
mark upon an assertion of Emmanuel Kant which has 
caused a great deal of confusion in philosophy. He 
asserted that there could be a proposition which would 
be at once synthetic and a priori, and he called it the 
synthetic a priori. Kant illustrates his discovery with 
examples. For instance, he draws upon arithmetical 
addition. The proposition three and two are five, 
3 + 2 = 5, is with him synthetic a priori : a priori, because 
it is absolute ; synthetic, because, he says, the predicate 
five, 5, adds on a new notion over and above three and 
two, 3 + 2. Let us see if the predicate adds a new idea. 
We repeat what we said before, that we do not reason 
with the mere sound of the voice or the mere appear- 
ance of marks on paper. What does the subject mean } 
3 means i + i + i. 2 means i -f i. 3 + 2 means i + 
I + I + I + I. 5 means i + i + 1 + i + i. Now put 
down the meaning of 3 + 2 = 5, and you have i + i + i 
+ 1 + 1 = 1 + 1 + 1 + 1 + 1. What is there in the 
predicate that is not in the subject.'' 



Article V. Extension and Comprehension. 

58. An Axiom. We have delayed to this point a very 
important consideration on the subject of ideas and terms. 
We have delayed it on account of its immediate use in 
the next article. In fact, we do not hesitate to say that 
the thorough understanding of the subject of the present 



JUDGMENTS, PROPOSITIONS. 35 

article is the key to philosophy. There is an old axiom 
in philosophy which runs thus : TJie greater the extejision, 
the smaller the compreJiension ; or TJie smaller the com- 
preJicnsion, tJie greater tJie extension ; or Widen tJie exten- 
sion, and you diminisJi the comprehension ; or Expand the 
comprehension, and yon narrow the extension. All mean 
the same thing. But what do they mean .-' 

59. Extension. The extension of an idea or a term 
refers to the number of individuals to which it can apply. 

60. Comprehension. The comprehension of an idea 
or of a term refers to the number of ideas or terms im- 
plied in said idea or term. 

61. Illustration. Take the idea, animal. It can apply 
to — that is, it extends to all individuals in which 
there is animal nature. But combine it with the idea 
rational, so as to have rational animal, or man. At 
once you shut out from its application all irrational 
animals. You cut them off from its extension. You 
narrow its extension. Why.-* Because you have ex- 
panded the comprehension. The idea man comprehends 
not merely animal but animal + rational. If you expand 
the comprehension by adding the term zvhite, so as to 
have white man, you will diminish the extension by 
cutting off all men who are not white. And so on. 
Every new idea added represents a new requisite in the 
object that is to correspond. The more you require in 
the objects, the fewer will they be found. 

Once more take the term animal. What is its com- 
prehension .'' What ideas does it imply .'' It implies 
sensitive oiganic material substance. Diminish the com- 
prehension. Take away the term sensitive. You have 
left organic material substance. At once you have 



36 THE LAWS OF THOUGHT. 

widened the extension so as to take in the whole vege- 
table kingdom. Diminish comprehension again. Strike 
out organic. There remains material substance. The 
extension is widened so as to take in all that is matter 
whether organic or not. Diminish the comprehension 
again. Strike out material. SiLbstance remains. The 
extension has been increased so as to reach into the 
spiritual world. 

.y^ Article VI. Extension of Propositions — 
' Quality. 

Universal — Collective — Particular — Singular. 

62. Extension. We have just spoken of extension in 
the abstract as contrasted with comprehension. In No. 
19 we saw that the same idea could be used with varied 
compass within the entire range of its extension. It 
may be singula?', particular, collective, universal. 

63. The Subject. The extension of a proposition de- 
pends upon the extension or compass of the subject as 
used in the proposition. The proposition is named 
accordingly singula?', particular, collective, universal. 
The following are examples. Singular : TJiis man is 
virtuous. Particular : Some man is virtuous. Some 
men are virtuous. Collective : TJie crovud is orderly. 
Universal : Angels are spirits. 

64. N.B. In speaking of terms and propositions we 
shall often not make a distinction between singular, col- 
lective and particular, but shall call them indifferently 
by the name particular as representing any term or 
proposition that is not universal. 



JUDGMENTS, PROPOSITIONS. 3/ 

65. The Predicate. To state clearly what we wish to 
say about the predicate, let us take four propositions, — 
two universal and two particular, — and let one of each 
kind be an affirmative proposition ; the other, a nega- 
tive. This will give us, for instance, the following : 

1. Cats are quadrupeds, (Universal Affirmative.) 

2. Birds are not quadruxteds. (Universal Negative.) 

3. This field is triangular, (Particular Affirmative.) 

4. Some roses are not red. (Particular Negative.) 

66. Universal Affirmative. The first proposition is uni- 
versal, because its subject is universal, i.e. taken in its 
entire extension. As to the predicate, quadruped, we do 
not directly allude to its extension. We merely assert 
that the idea quadruped enters into the comprehension 
of the idea cat. And as cat here is universal, taking in 
each and every cat, we do state that quadruped is at 
least coextensive with cat. But we do for a fact know 
that quadruped has a wider extension than cat, that cat 
covers only a part of the extension of quadruped. Only 
some quadrupeds are cats. Hence, when we speak 
according to our knowledge and say that all cats are 
quadrupeds, we wish to say that some quadrupeds are cats, 
or the idea, cat, extends to some individuals, not to all 
individuals in the extension of quadruped. Quadruped, 
therefore, in the discussion of the proposition is to be 
regarded as a pajiicular term. As these remarks hold 
good for all universal affirmative propositions (one class 
excepted), we formulate the law : TJie Predicate in a uni- 
versal affirmative proposition is a particular term. 

67. One Exception. The one exception is, when the 
predicate is the exact essential definition of the subject. 
Thus in the proposition, Man is a rational animal, the 



38 THE LAWS OF THOUGHT. 

predicate, rational animal, is the essential definition of 
the subject, man. It is synonymous with man. Hence it 
is precisely coextensive with the subject. We can say, 
Man is a rational animal, or Rational animal is man. 
But though we say, Cat is quadrnped, we cannot say. 
Quadruped is cat. Qnadruped may be tiger or elephant. 
Rational animal, however, cannot be anything but man. 

68. Universal Negative. In the second proposition. 
Birds are not qitadrupeds, the subject is universal, and 
hence, too, the proposition. By denial we separate the 
idea qnadruped from the comprehension of the idea bird. 
So that wherever the idea bird is applicable, in its entire 
extension, there the idea quadruped is excluded. Now, 
knowing that quadruped can have its own extension, the 
proposition implies that bii'd and quadruped extend to 
two distinct classes of individuals. To say that birds are 
not quadrupeds is the same as saying that no individual 
bird is a quadruped. Not one bird can be found in the 
class quadruped. Not one quadruped can be found in 
the class bird. If it could, some bird would be a quad- 
ruped. What is this but to exclude quadrupeds in its 
entire extension, that is, as a universal, from the entire 
extension of the subject.-' As the same remarks hold 
good for all universal negative propositions, we formulate 
the law : The Predicate in a imiversal negative proposi- 
tion is a universal teimi. 

69. Particular Affirmative. In the third proposition, 
This field is triangular, the subject is particular. Hence 
the proposition is particular. Referring to our knowl- 
edge of things, we shall find that the predicate, triajtgu- 
lar, is used in a particular sense. We do not predicate 
of this field all that is or may be triangular, the entire 



JUDGMENTS, PROPOSITIONS. 39 

extension of triangular; but only this particular case of 
triangular. This field is one of the things embraced in 
the extension of triangular. Triangular, hence, is used 
in the particular sense. These remarks hold good for 
every particular affirmative proposition. Hence the 
law : TJic Predicate in a particular affirmative proposi- 
tion is a particular term. 

70. Particular Negative. In the fourth proposition, 
Some roses are not red, the extension of the subject, only 
some roses, is particular. Hence the proposition is par- 
ticular. The predicate red, however, is used in the 
universal sense. We affirm that redness is not found 
in the comprehension of some certain roses. No one of 
these some certain roses is to be found in the entire 
extension of things that are red. We separate the 
entire extension of things that are red from these some 
certain roses. Hence, in our denial of red as applicable 
to some roses, we use it in its entire extension, or as a 
universal. These remarks hold good for every particu- 
lar negative proposition. Hence the law : The Predi- 
cate in a particular negative proposition is a universal 
term. 

71. Two Laws. Now let us put the four laws together 
and make two of them. The first and third will give us 
this : The predicate in an affirmative proposition is used 
as a particular term, i.e. according to part of its extension. 

The second and fourth law will give us this : TJie pred- 
icate in a negative proposition is used as a universal 
term, i.e. according to its entij'e extension. 

72. Affirmative and Negative. We have not thought 
it necessary to state explicitly heretofore that every 
proposition must be either affirmative or negative. For 



40 THE LAWS OF THOUGHT. 

all needs, up to the present, this was sufficiently implied 
in the definitions oi judgment "dsidi proposition. 

73. Negative Particle. We call attention now to the 
fact that, in the negative proposition, the negative par- 
ticle need not necessarily stand between the subject and 
the predicate. To say, Bi^^ds are not qitadmipeds, is the 
same as saying, No bird is a quadruped. Both are neg- 
ative and are understood as such. We have not to 
question the arbitrary constructions of language. Still 
be it understood that, in order to have a negative proposi- 
tion, the language must be capable of such construction 
that the negative particle not may be construed with the 
copula, is, a7'e, so as to form with it one piece that shall 
be, not as a link between subject and predicate, but as 
a wall of separation. This is the case in the example 
given above. But the following proposition is affirma- 
tive : Not to complain in adversity is a mark of a great 
soul. We may indeed say, To complain in adversity -is 
not a mark of a great soul ; but the two propositions are 
not identical in meaning, for we turn the predicate from 
a particular into a universal. However, we may say, 
A mark of a great soul is not-to-complain-in-adversity. 
Here the negative particle, though next to the copula, is, 
does not form one piece with it : it forms a piece of the 
predicate. The proposition is affirmative. 

74. Quantity and Quality. The extension of a propo- 
sition, universal, particular, etc., is referred to as its 
quantity. The form, affirmative or negative, is referred 
to as its qttality. 



JUDGMENTS, PROPOSITIONS. 4 1 

Article VII. Related Propositions. 
Conversion — Equivalence — Opposition. 

75. Three Relationships. We now pass on to consider 
the relations that may exist between certain propositions. 
The relation between two propositions — when there is 
any relation at all — will be one of convertibility, of 
equivalence or of opposition. 

76. Conversion. A proposition is said to be converti- 
ble into another when the subject can be made predicate 
and the predicate subject without loss of truth in the new 
proposition. Thus the proposition, No man is an angel, 
is convertible into No angel is a man. There are three 
ways of converting propositions. We may keep the 
quantity and quality unchanged ; or we may change 
quantity only ; or we may change quality only. The 
first is called simple conversion ; the second, conversion 
per accidens ; the third, conversion by contraposition. 
Without minding these traditional names, we shall 
exemplify the three conversions. 

Quantity and quality unchanged. This conversion 
may take place in propositions where subject and predi- 
cate are both universal or both particular — that is, in 
universal negative and particular affirmative ; as also, in 
propositions where the predicate is the es-sential defini- 
nition of the subject, since the two are coextensive. 
Thus, No man is an angel is convertible into No angel 
is a man. This field is square is converfible into This 
square thing is afield. Man is a rational animal is con- 
vertible into The rational animal is man. 

Quantity chajtged. This kind of conversion may be 
applied to universal affirmative and universal negative 



42 THE LAWS OF THOUGHT. 

propositions. In the universal affirmative, All plants are 
substances, the predicate is particular. If we make it 
subject, we have Some substajues are plants. The uni- 
versal negative, No man is an angel, we saw above may 
be converted into No angel is a man. This being uni- 
versal, applies to each individual in the extension of the 
subject ; hence we have. This angel is not a man. 

Quality changed. This kind of conversion may be 
used upon the universal affirmative and the particular 
negative. The universal affirmative. Cats are quadru- 
peds, tells us that cats are altogether within the extension 
of quadruped. Outside of the extension of quadruped, 
cats are not to be looked for. Hence the proposition is 
convertible into What is not quadruped is not a cat. In 
the particular negative. Some roses are not red, red is 
universal in its extension. Hence outside of the exten- 
sion of red there are some roses; or. Some things not 
red are roses. 

77. Equivalence or EquipoUence. A proposition is said 
to be equivalent to (equal in value) or eq?npollent with 
(equal in weight) another when it means the same thing 
as the other, there being no conversion of subject and 
predicate. A proposition is turned into its equipollent 
in various ways by the use of the negative particle. 
Thus, Every man is mortal is equivalent to No man is 
not moj'tal, etc. 

78. Opposition. To explain what is meant by opposi- 
tion, let us take the universal affirmative proposition. 
Every tnan is just. In order merely to contradict this 
it would be sufficient to say, Some man is not just. 
Now take the universal negative proposition, No man 
is just. To contradict this it is enough to say. Some 



JUDGMENTS, PROPOSITIONS. 43 

)}ian is just. We have in both cases an opposition 
between a universal and a particular, an affirmative and 
a negative. There is opposition in both quantity and 
quality. The opposition is one of contradiction. Propo- 
sitions so related are called contradictories. Both cannot 
be true, simultaneously ; nor can both be false, simulta- 
neously. If it be true that all men are just, then it is 
false that some man is not just. 

Opposition in qnality only. When two universal prop- 
ositions are opposed in quality, i.e. one being affirm- 
ative, the other negative, as. All men are Just and No 
men are Just, there is not merely a contradiction of a 
sweeping statement. There is a sweeping statement to 
the contrary. The contradiction covers each individual 
in the extension of the opposite proposition. The oppo- 
sition is one of contrariety. The propositions are called 
contraries. Both cannot be true at the same time, be- 
cause each one contradicts every individual case of the 
other. However, both may be false. They may both 
claim too much in opposite directions. 

The particular propositions implied in these two uni- 
versals, that is, the particulars, Some mati is Just and 
Some man is not Just, as opposed to one another in 
quality, are called sitbcontraries. Both may be true, 
since their contradictories, the universals, may both be 
false, may both assert too much. Both particulars, 
however, cannot be false ; for if both were false, then 
their contradictories, the universals, would both be true. 

Opposition in quantity only. This is the opposition 
between a universal and particular affirmative or a 
universal and particular negative, as, All men are Just 
and Some man is Just ; or N^o man is Just and Some 
man is not Just. There is in reality no opposition here. 



44 THE LAWS OF THOUGHT. 

The particular is implied in the universal. It is a 
subaltern of the universal. Hence, for the sake of a 
name, propositions so related, the universal and its 
implied particular, are called subalterns. If the uni- 
versal is true, the particular is true. If the universal 
is false, the particular may still be true. From the truth 
or falsity of the particular we can form no judgment 
about the truth or falsity of its universal. 

79. Diagram. Now look at the following diagram : 

Contrary. 
I. All men are just (iZ/wV. ^^.). 2. No man is just {Univ. Neg.^. 

^ °4> ^ ^ 

t-i X t-i 

3. Some man is just (Par^. ^^.). 4. Some man is not just (/*ar^.iV>^.). 

SUBCONTRARY. 

I and 2 are contraries ; 3 and 4 are subcontraries ; 

1 and 4, also 2 and 3, are contradictories ; i and 3, also 

2 and 4, are subalterns {i and 2 being called subalternant, 

3 and 4 their subalternates). 

It is clear that if i is true, 3 is true ; and that if 2 is 
true, 4 is true. But we cannot conclude from 3 to i nor 
from 4 to 2. 

I and 4 cannot be both false. One must be true, and 
the other false. The same is to be said of 2 and 3. 

3 and 4 may be both true, or one true and the other 
false. Both cannot be false. 



CHAPTER IV. REASONING, ARGUMENT. 



Article I. The Syllogism. 

Argument — The Syllogism — Analysis of Argument — Middle and 
Extremes. 

80. Reasoning and Argument. We have seen how the 
idea is the element of the judgment, and thus the term, 
the element of the proposition. We have now to see 
how an argument is constructed out of propositions. 
We defined Reasoning (ii) to be an act, or a series of 
acts, by which the mind compares the truths expressed 
by two judgments, and in that comparison perceives 
implied a third truth, which it accordingly expresses 
mentally in a third judgment. This process, we said, 
regarded as mere mental working, is called reasoning. 
Regarded as knowledge contained in the third judgment, 
pronounced as having been implied in the two others, 
we called it inference or argument. The propositions 
which, taken together, represent in language the knowl- 
edge and its process, we also called argument. We 
shall use the word argument in this latter sense. 

81. Styles of Argument. There are indeed many com- 
binations of propositions which are used as language- 
representations of the process of reasoning, many styles 
of argument. Different names are given to them, accord- 
ing to the variety of structure. We have the Syllogism, 

45 



4-6 THE LAWS OF THOUGHT. 

tke Enthymeme, the Sorites, the Polysyllogism, the Epi- 
chirem, the Dilemma. All, however, are reducible to the 
syllogism, which is the nearest approach language can 
make towards exhibiting the working of the mind in 
reasoning. Not that we alwa,ys, or usually, argue, in 
speaking or writing, with completed syllogisms. We 
abbreviate. However, we must study the syllogism in 
its completeness. We begin with it. A few words at 
the end of this chapter will then suffice to explain the 
other styles of argument. 

82. The Syllogism. The syllogism is an argument 
made up of three propositions so connected that if the 
first two be admitted, the third must, likewise, be 
admitted. Thus, 

Every jtlant is a substance; 
But the verbena is a jy^cint. 
Therefore, The verbena is a substance, 

83. Antecedent ; Consequent ; Premisses. The first two 
propositions taken together are called the antecedent. 
The third proposition is called the consequent. In the 
antecedent the evidence is stated. In the consequent 
the verdict is given. The two propositions of the ante- 
cedent are commonly called premisses (put before). The 
first is called the major premiss ; the second, the minor 
premiss. For brevity's sake they are styled the major 
and the minor. The original meaning of major and 
minor, and the reason for the use of the terms, will be 
explained in the next article. 

84. Consequence. If the consequent does really fol- 
low from the premisses, we have what is called a conse- 
quence, by which we mean that the assertion contained 



REASONING, ARGUMENT. 47 

in the consequent is a consequence of what was laid 
down in the premisses. If an argument is proposed to 
us in which the consequent does not follow as a conse- 
quence, the argument must be regarded as faulty. 
Hence, 

{a) If both the premisses be true, and the argument 
be rightly constructed, the consequent, called also the 
conclusion, must be true : the consequent must be 
admitted. 

{b) The conclusion, or consequent, may indeed be a 
true proposition, as stated, and taken by itself ; and, still, 
on account of a flaw in the structure of the argument, it 
may not really follow from the premisses. In this case 
we may admit it as an independent proposition. We 
admit the consequent, but we deny the consequence. 

85. Axioms. We repeat here two axioms stated in 
No. II. They are the bases upon which every argu- 
ment must rest. If the conclusion is an affirmative 
proposition the argument rests upon this axiom : /;/ tJie 
sense in wJiicJi two things are the same as a tJiird thing, 
in the same sefise are they the same as one another. If 
the conclusion is a negative proposition, the argument 
rests upon this axiom : In the sense in ivhich tzvo things 
arc, the one the same as a third thing, the other differ- 
ent from it, in the same sense are they different from one 
another. 

86. Analysis of Argument. Now look at the argument 
given above, namely : 

Antecedent \ ^^'^''>' P'^"^ '^ ^ substance (Major Premiss), 
i But the verbena is a plant (Minor Premiss). 
Consequent or ^ Therefore, the verbena is a substance (Conse- 
CONCLUSION ( quence). 



48 THE LAWS OF THOUGHT. 

You will find 

1 . That it contains but three terms, — plant, substance, 
verbena. 

2. That one of the terms, plant, occurs twice in the 
premisses, — once in the major, and once in the minor. 

3. That the two other terms, substance, verbena, occur 
each once in the premisses, one in the major, and one in 
the minor ; and that they both occur in the conclusion. 

4. That the term plant is not found in the conclusion. 

5. That thus each term occurs twice in the argument. 

6. That the term plant, which occurs twice in the 
premisses, is there compared with the two others ; with 
one in the major, with the second in the minor. 

7. That a certain relationship having been discovered, 
in the premisses, between verbetia and substance, by 
means of the aforesaid comparison, this relationship is 
declared in the conclusion. 

87. Middle and Extremes. The term that is used as a 
standard of comparison between the two others is called 
the middle term; or for brevity, the middle: the two 
others are called the extreme terms or the extremes, one 
the major and the other the minor extreme. We shall 
have to speak of this subject presently. 



Article II. Figures and Moods of the 
Syllogism. 

Major and Minor Premiss — Major and Minor Extreme — Middle 
Term. 

88. Major ; Minor ; Middle. We spoke, in the last arti- 
cle, of major and minor premiss, major and minor ex- 
treme, and of the middle. We called the first premiss 



REASONING, ARGUMENT. 49 

the major, and the second premiss the minor, and we 
shall continue to call them so. But the first premiss is 
not always really the major, in the original meaning 
attached to the word ; nor, in the same original meaning, 
is the second always the minor. According to the orig- 
inal use of the words, the major premiss is the premiss in 
which the middle is compared with the major extreme ; 
and the minor premiss is the one in which the middle 
is compared with the minor extreme. The major ex- 
treme is the one whose extension is greater than that of 
the middle. The minor extreme is the one whose exten- 
sion is less than that of the middle. This is how the 
middle came to be called middle ; because, its extension 
is between the extensions of the two other terms. 

There is only one style of syllogism in which the mid- 
dle is a real middle, as just explained. This is in the 
most obvious style of construction of the syllogism (No. 
89) ; and it is from this that the names have grown into 
common use, and are applied to all syllogisms, in the same 
way, regardless of construction. We call the premiss 
put first, the major ; that put second, the minor : and 
we never speak of the extremes as major and minor. 
This leads us to the question of figures of the syllo- 
gism. 

By Figures are meant merely the various combina- 
tions of the extremes with the middle, in the premisses. 

89. First Figure. The First Figure is the one that we 
have just spoken of. In this, the middle is made the 
subject of the premiss containing the major extreme, and 
this premiss is placed first : it (the middle) is made the 
predicate of the premiss containing the minor extreme, 
and this premiss is placed second. Thus : 



50 



THE LAWS OF THOUGHT. 



Anhnals are living beings ; (Major Premiss.) 
But lions are animals. (Minor Premiss.) 
Therefore, Lions are living beings. 

Here the middle, animals, has less extension than 
living bei7igs {va2i]or extreme), and greater extension than 
lio7is {minor extreme). The following squares will show 
how one is included in the extension of the other, and 
how easily the argument proceeds on that account. 





LIVING BEINGS 








ANIMALS 








LIONS 

Minor 

Extreme 






Middle 






Major Extreme 





As our argument was stated, we proceeded within the 
extension of living beings to find animals, and then 
within the extension of animals to find lions ; thence to 
conclude that lions were within the extension of living 
beings, and that living being could be predicated of lion. 
The minor premiss might be placed first, and the major 
premiss second. Thus : 

Ziions are animals; 
But animals are living beings. 
Therefore, Lions are living beings. 

In this, we proceed from the minor extreme up through 
the middle to the major extreme. 



REASONING, ARGUMENT. 



51 



90. Second Figure. We remark, again, that outside of 
the F'irst Figure, what we call middle is really not a 
middle, in the true sense, but only in the sense that it is 
taken as a term of comparison between two other terms. 
Still we keep the name, middle ; and the other terms 
are called simply the extremes. 

In what we call the Second Figure, the middle term is 
used as predicate in both premisses. Thus : 



Therefore, 



Every man is mortal; 
li'o angel is mortal. 
No angel is a man. 



Here mortal is the middle. Man is truly minor with 
reference to mortal. But we cannot say that Angel is 
major with reference to mortal. Angel is simply ex- 
cluded by, and excludes, mortal, and hence, excludes 
the minor contained in mortal. 





MORTAL 






MAN 











ANGEL 



91. Third Figure. In what we call the Third Figure 
the term of comparison is the subject of both the first 
and second premiss. Thus : 



Therefore, 



Every plant is substance; 
Every 2ilfttit is material. 
Some substance is material. 



52 



THE LAWS OF THOUGHT. 



Here the term plant has less extension than either of 
the other two. The meaning of middle is lost. The 
extremes are both major. 



9^ 








PLANT 








% 



Both substance and material cover the extension of 
plant, and hence partly coincide, i.e. at least to the 
extent of plant. This will suffice on the subject of 
Figures. 

What we have to remember is this, that in practice 
the premiss which stands first we shall call major ; the 
premiss that stands second, minor ; the term that is 
used as the standard of comparison, middle ; the two 
other terms, extremes. 

92. Moods of the Syllogism. By moods of the Syl- 
logism are meant the various combinations that may be 
made in the premisses, of universal, particular, affirma- 
tive and negative propositions. We should derive no 
practical utility from a discussion of the sixty-four 
possible combinations, few of which give a correct 



REASONING, ARGUMENT. 53 

argument. For the sake of a completeness, which is 
not necessary, we subjoin the following remarks on 
figures and moods. 

I. There is a Fourth Figure, which is little used, and 
which it is well to avoid in argumentation. In it the 
middle is made predicate of the major proposition and 
subject of the minor. 

Every tree is organic; 
Evertjthiuff organic is substance. 
Therefore, Some siihstance is a tree. 

This, it will be noticed, is the same as the First Figure 
with the position of subject and predicate inverted in 
the conclusion, and the proposition accordingly changed 
from the universal, Everj/ tree is a substance, to the 
implied particular. 

2. If now we take the four kinds of propositions. 
Universal Affirmative, Universal Negative, Particular 
Affirmative and Particular Negative, and make all the 
possible combinations of them that can be made in each 
of the Four Figures, we shall find that there are sixteen 
possible combinations in each figure, or sixty-four in 
all, — simply regarding the position of the middle and 
taking no account of the validity of the conclusion. 
These sixty-four combinations are called the Moods of 
the Syllogism. If we take into account the validity of 
the conclusion as proceeding from the premisses, we 
shall find that only nineteen of the sixty-four combina- 
tions make correct arguments. These nineteen Moods 
are thus distributed: 4 in the First Figure; 4 in the 
Second ; 6 in the Third ; and 5 in the Fourth. 

We shall be able to decide upon the correctness of any 
combination from the laws of the syllogism which follow. 



54 THE LAWS OF THOUGHT. 

Article III. Laws of the Syllogism. 

93. Scope of the Laws. We are now prepared to 
formulate the laws which must govern the construction 
of the correct syllogism. These laws have reference to 
the number of terms, the extension of terms, the place 
of the middle term, the quantity and quality of premisses 
and conclusion. 

94. First Law. Three Terms. There must be three, 
and only three, terms, and they mitst be only tJu^ee in 
meaning. This is evident from what has been said : 
that the conclusion of a syllogism is simply a declaration 
of identity or difference between two terms (objectively), 
which identity or difference was implied by the compari- 
son of these terms (objectively) with a third term in the 
premisses. It is not enough, therefore, to have the 
terms three in mere sound or written appearance. They 
must be three in meaning (objectively). Our reasoning 
is not upon sounds of the voice or upon printed letters ; 
it is upon that which is represented both by the idea and 
by the spoken and written word. If we say : 

Stores are tvareJiouses, 
Stores can be eaten, 
Therefore, Warehouses can he eaten, 

we have three terms in sound and writing ; but we have 
four in meaning; and thus there is no syllogism. If 
we say : 

Eye is the organ of sight, 

I is a personal j^^^onoun, 
Therefore, The organ of sight is a personal pronoun, 



REASONING, ARGUMENT. 55 

the terms are three in sound, but four in meaning, as in 
writing. There is no syllogism. If we say : 

Andrew Jachson is one of the Presidents ^ 
Franklin Pierce is one of the Presidents, 
Therefore, Andretv tfackson is Franklin Pierce, 

we have four terms, in meaning; because, One-of-the- 
Prcsidents is taken in two di\'iiQXQXi\. particular senses. 

95. Second Law. Extension of Extremes. Neither ex- 
treme may have a greater extension in the conclusion tJian 
it had in the premisses. This is a consequence, or an 
application, of the first law. For if a term in the conclu- 
sion embraces more individuals than it did in the prem- 
isses, it is really a fourth term, because it stands for 
something not meant in its first use. In the following, 

Tobacco is a j)lant, 
Tobacco is narcotic, 
Therefore, Plants are narcotic, 

the term plant, as predicate of an affirmative proposi- 
tion in the major, is a particular term ; whilst, in the 
conclusion, as subject of the universal proposition, it is 
taken according to its entire extension. There are four 
terms : hence no syllogism. 

96. Third Law. Extension of the Middle Term. The 

middle term must be used once, at least, according to its 
entire extension, i.e. as jiniversal. The reason : for if 
it be twice a particular, each use may embrace totally 
different sets of individuals, totally distinct sections of 
the entire extension. This would give two different 



56 THE LAWS OF THOUGHT. 

meanings for the middle, and hence, four terms. If 

we say : 

Tigers are animals, 

Lions are animals, 

we may not conclude 
Therefore, Lions are tigers. 

The middle term, animals, is twice particular, covering 
distinct sections of the entire extension, animals. It is 
really two terms. 

An objection. How, then, can the middle term be 
used once universally, and once particularly } Will not 
this give us four terms } No ; because what is said of 
the term taken universally, i.e. standing for all individ- 
uals, and for each and every individual in the extension, 
can also be said of this or that individual taken sepa- 
rately. An example : 

Spirit is indivisible; 
The soul is spirit. 
Therefore, The soul is indivisible. 

In the major, spirit is universal. We say that all 
spirits are indivisible ; hence, that each particular spirit 
is indivisible. In the minor, we simply call one particu- 
lar spirit by its name. In the major we said ajiy spirit. 
In the minor we make the choice that has been offered 
us directly in the major. There are only three terms. 

Of course the middle may be used twice universally. 
In this case, both premisses will have to be affirmative, 
and the conclusion will be particular. Thus : 

All fishes are sensitive ; 
All fishes are shy. 
Therefore, Some things sensitive are shy. 



REASONING, ARGUMENT. 5/ 

In these premisses the extremes are predicates of affir- 
mative propositions, and hence are particular. There- 
fore, by the second law, they must have a particular ex- 
tension in the conclusion. This last example belongs to 
the Third Figure. 

97. Fourth Law. Place of the Middle Term. The mid- 
dle term must not be found in the eonelusion. This is 
evident from the nature of the syllogism. Two terms 
are compared, separately in the premisses, with a third 
term, in order that their identity, or disparity, may be 
expressed in the conclusion ; the middle term being 
rejected, after its use as a standard of comparison. 

98. Fifth Law. Affirmative Conclusion. Tiuo affirma- 
tive premisses demand an affirmative eonelusion. For if, 
in the premisses, we implicitly affirm the identity of the 
extremes, we cannot deny that identity, explicitly, in the 
conclusion. 

99. Sixth Law. Negative Conclusion. One premiss affir- 
mative and one premiss negative demaiid a negative 
conclusion. For, in the premisses, we implicitly deny 
identity between the extremes, by declaring that one is 
identical with the middle, and that the other is not. 
Hence we have but to deny their identity, explicitly, in 
the conclusion. 

100. Seventh Law. No Conclusion. From two negative 
premisses zve can drazv no conclusion. If we say, 

Scipio is not a carpenter, 
Scipio is not a Russian, 

there is no conclusion to be drawn. We have done 
nothing but to place Scipio outside the extension of the 



58 



THE LAWS OF THOUGHT. 



two extremes ; but there is nothing from which to infer 
whether there be, or be not, Russians among the car- 
penters, or carpenters among the Russians. All we can 




Carpenters 



Russians 



say is what has been affirmed explicitly, that Scipio is 
neither a Russian nor a carpenter. 

The same holds if the premisses are two negative uni- 
versal propositions. All the terms will be universal. 
The middle term, in its entire extension, will be outside 
the entire extension of each extreme. 

No star is an elephant; 

No elephant is a tvJieelbarrow. 

No conclusion. 

101. Eighth Law. No Conclusion. F;^^. two particu- 
lar premisses we can draw no conchLsion. For they will 
be either, i, both negative; or 2, both affirmative; or 3, 
one affirmative and one negative. 

First case: both negative. This is settled by the 
seventh law. 

Second case : both affirmative. In this case the sub- 
jects are particular, as we have particular propositions ; 
and the predicates are particular because the proposi- 
tions are affirmative (No. 71). Hence the middle term 
is not taken once universally, and the third law is 
broken. 

Third case : one affirmative and one negative. Then, 
according to the sixth law, the conclusion will have to 



REASONING, ARGUMENT. 59 

be negative. The predicate of the conckision will thus 
be universal (No. 71). As this predicate is one of the 
extremes, it must, by the second law, be universal in the 
premisses. But in the premisses there is only one place 
for a universal term ; that is, as predicate of the negative 
premiss. The particular affirmative premiss cannot have 
a universal term, and the subject of the particular nega- 
tive premiss must be particular. Now if this one place 
in the premisses where a universal term can be, be taken 
by one of the extremes, the middle term will not be, 
cannot be, used universally at all. Hence this third 
case is an impossibility, and the eighth law holds. 

We must here make an exception for the case w^here 
both premisses are singular. In this case there may be 
a conclusion. Thus : 

Mars is a planet; 
Mars is uninhabited. 
Therefore, One planet is uninhahited. 

The reason is that the term, Mars, being applicable 
to one individual only must be used in its entire exten- 
sion, and hence, as subject in both premisses, has the 
value of a universal : so that the two premisses may be 
treated as universals. 

102. Ninth Law. Particular Conclusion. If one premiss 
be particular, the conclusion must be particular. Of course, 
by the eighth law, one premiss must be universal. The 
possible cases with one premiss universal, and one par- 
ticular, are : 

1. With both premisses affirmative ; 

2. With one premiss affirmative, the other negative ; 
and in the second case we have an alternative. We 
may take a universal affirmative and a particular nega- 



6o THE LAWS OF THOUGHT. 

tive ; or we may take a universal negative and a par- 
ticular affirmative. 

1. Making both premisses affirmative, we shall have, 

Universal Affirmative (with subject utiiversal and predicate 

particular) ; 
Particular Affirmative (with subject particular and predicate 

particular) . 

There is but one place for a universal term. This 
must be for the middle {TJm'd Law). The extremes 
are both particulars in the premisses. Hence the subject 
of the conclusion must be particular {Second Law) ; and 
the conclusion, a particular proposition. 

2. Making one premiss negative and one affirmative, 
we shall have either 

Universal Affirmative (with subject universal and predicate 

particular) ; 
Particular Negative (with subject particular and predicate 

universal) . 

Or, 

Universal Negative (with subject universal and predicate 

universal) ; 
Particular Affirmative (with subject particular and predicate 

particular) . 

In either case there are two places for a universal. 
One place must be for the middle {Third Law), The 
other place will be for the extreme which is predicate of 
the conclusion ; the conclusion being negative, since 
one premiss is negative. The subject of the conclusion 
must therefore be an extreme, used particularly in the 
premisses. It must be particular in the conclusion 
{Second Law), and will make the conclusion a particular 
proposition. 



REASONING, ARGUMENT. 6 1 

103. Caution. Here we leave the laws of the syllo- 
gism. Certain correct syllogisms may be adduced which 
may seem to contravene the laws. But if the propo- 
sitions of the syllogisms thus presented be examined, 
it will be seen that certain propositions, apparently 
particular, are really universal ; and certain propositions, 
apparently negative, are really affirmative, or vice versa. 
But let it be kept in mind that we reason not with mere 
words as they sound or appear on paper, but with what 
they stand for ; and words, by tricks of grammar, may 
be made to obscure a thought in the presentation. In 
the same way, syllogisms with ill-drawn conclusions 
may be made to appear in keeping with the laws. But 
study the sense of the propositions. 



Article IV. Some Species of the Syllogism. 
Conditional — Conjunctive — Disjunctive. 

104. Simple and Compound Syllogisms. We have hith- 
erto, for the sake of clearness, given examples of syllo- 
gisms composed of simple categorical propositions only. 
Such syllogisms are, as their component propositions, 
called simple. One compound premiss is sufficient to 
make the syllogism compound and equal to as many 
simple syllogisms as there are simple categorical propo- 
sitions compounded into that premiss. We do not 
propose to treat of compound syllogisms. We should 
never end. Attention is called here to three complexi- 
ties in the syllogism, to which we alluded in No. 49. 

105. Conditional Syllogisms. In these the major is a 
conditional proposition (46); for instance, this, If tJiey 



62 THE LAWS OF THOUGHT. 

are studying logic, they are training their minds. The 
first member of the conditional proposition is called the 
condition ; the second, the consequent. The minor may 
affirm the condition categorically : 

They are studying logic. 

Then the conclusion must affirm the consequent cate- 
gorically : 

They are training their tninds. 

Or the minor may deny the consequent : 

TJiey are not training tlieir minds. 

Then the conclusion denies the condition : 
They are not studying logic. 

Note. i. The denial of the condition will not necessitate the 
denial of the consequent. This (the consequent) may be true for 
other reasons. In the present instance they might be studying 
grammar or geometry without logic ; and they would still be train- 
ing their minds. 

2. Hence affirmation of the consequent does not always necessi- 
tate affirmation of the condition. There may, as we said, be other 
conditions from which it (the consequent) would follow. They may 
in the present instance be training their minds by studying other 
matters than logic. 

106. Conjunctive Syllogisms. In these, two incompati- 
ble propositions are proposed in the major by means 
of a conjunctive proposition (47). The minor denies 
one, and the conclusion affirms the other. Example : 

N'o man can spend all his money on drink and still 

support his family ; 
But he spends all his inoney on drink. 

Therefore, 

Se does not support his family. 



REASONING, ARGUMENT. 6^ 

What we said about looking into the meaning of the 
proposition and not being deceived by tricks of construc- 
tion is of service here. The conjunctive proposition is 
really equivalent to a conditional, thus. If a man spends 
all his money on drink, he is unable to support his fafnily; 
and with regard to affirmation and denial of condition 
and consequent must be treated as such. 

107. Disjunctive Syllogisms. In these the major puts 
all the alternatives of a case in the disjunctive proposi- 
tion (48). If the minor makes choice of one, the conclu- 
sion will be the denial of all the others. If the minor 
denies all but one, that one will be affirmed in the 
conclusion, etc. 

Example : He is either just fifty or under fifty or past 

fifty; 

But he is just fifty ; 
Therefore, He is neither under fifty nor past fifty : 
Or JBut he is neither under fifty nor 2>nst fifty ; 

Therefore, He is just fifty : 
Or But he is not just fifty ; 

Therefore, He is either under fifty or jyast fifty. 

In the last case, as we have three possibilities, and the 
minor denies one only, the two others remain as a dis- 
junctive proposition in the conclusion. This form of 
syllogism may also be reduced to the conditional with 
one member positive and the other negative. If he is 
under fifty, he is neither just fifty nor past fifty. 

The conjunctive syllogism is useful in controversy and 
investigation. But it is, at the same time, capable of 
treacherous application for the spread of error in history 
and physical science, by the use of disjunctive majors 
which are not complete. The disjunction should state 



64 THE LAWS OF THOUGHT. 

all the possibilities of the case. The members should 
have marked lines of division, and not run into one 
another. All the members may not be true; neither 
may all be false. 



Article V. Other Styles of Argument. 
Enthymeme — Sorites — Polysyllogism — Epichirem — Dilemma. 

108. Argument Abbreviated. We said (No. 81) that 
when we write and speak we do not always, nor even 
usually, carry on an argumentation with completed 
syllogisms. We abbreviate. The various methods of 
abbreviation give us various styles of argument, which 
have, respectively, their proper names. 

109. Enthymeme. If we drop one premiss in the syllo- 
gism, the argument is called an enthymeme. Example : 

All liquids will flow ; 
Therefore, This tar will flow. 

We have dropped one evident premiss, this tar is liquid, 
to avoid being tiresome. 

Enthymeme originally meant a probable argument ; 
but, by a mistake as to its derivation, it came to be 
applied to the argument where one premiss is kept in 
the mind. In this sense alone is the word now used. 

110. Sorites. {Piled-np argument.^ When we put 
down three or more premisses and, then, one conclusion 
following from them, the argument is called a Sorites. 
It abbreviates by dropping intermediate conclusions. It 
presumes the evidence of the conclusion after the first 
two premisses, and adds a third premiss as a minor to 



REASONING, ARGUMENT. 65 

the second premiss considered as a major ; then a fourth 
premiss as a minor to the third premiss considered as a 
major, etc. Thus : 

He who desjyonds ceases to labor; 

He who ceases to labor makes no progress ; 

He who maUes no progress does not reach the end. 

Therefore, 

He tvho desponds does not reach the end. 

It is easy to see that this is an abbreviation of two 
syllogisms. Thus : 

He ivho desponds ceases to labor; 

He who ceases to labor makes no jtrogress. 

Therefore, 

He ivho desponds makes no progress. 

The next syllogism begins with this conclusion as a 
major : 

He who desponds m,akes no jrrogress ; 

He who makes no progress does not reach the end. 

Therefore, 

He tvho desponds does not reach the end. 

As the Sorites involves so much argument, and pro- 
ceeds so rapidly, we must be cautious with an adversary 
who uses it. The Sorites may be drawn out to any 
length. Each implied syllogism must observe the laws 
of the syllogism. 

111. Polysyllogism. If we argue with a chain argu- 
ment, as in the Sorites, but in such a way that we bring 
out the intermediate conclusions, not explicitly tzvice as 
above, but once, to be used, simultaneously, as conclusion 



66 THE LAWS OF THOUGHT. 

to the two preceding premisses, and as major to a follow- 
ing minor, our argument is called a Polysyllogis7n. The 
preceding example, as a polysyllogism, will be : 

He who desponds ceases to labor ; 

He who ceases to labor inaTces no progress. 

Therefore, 

He who desjionds makes no jyrogress; 

He who makes no 2)rogress does not reach the end. 

Therefore, 

He who desponds does not reach the end. 

112. Epichirem. If a premiss, or even each premiss, 
requires proof, and the proof is attached to it immedi- 
ately, whether in substance or in full, the argument is 
called an Epichirem {taking in hand the doubted premiss 
at otice). Example : 

One who denies the existence of God and a future 
life cannot be trusted in society ; because he ad- 
mits no inotive to restrain him frotn evil when 
he can do the evil without tetnporal inconven- 
ience. 

But the atheist denies the existence of God and a 
future life. 

Therefore, 

He cannot be trusted in society. 

113. Dilemma. The Dilemma is a double argument 
in the compass of a single syllogism. It may be even 
triple, quadruple, etc. The major is a disjunctive prop- 
osition. The minor takes up each member of the dis- 
junction, separately, and an equally satisfactory conclu- 



REASONING, ARGUMENT. 67 

sion is drawn from whichever member is chosen. Thus 
a schoolboy might argue, to escape his evening study : 

To-inorrow morning it tvill he either raining or not 
raining. 

Jf it he raining, I will liave an excuse to stay at 
home. If it he not raining, I can use my per- 
mission to take a day at the fair. 

Therefore, 

Wliatever the weather may he, I shall not have to 
go to school; and hence I need not study my 
lessons to-night. 

The Dilemma is sometimes a very useful form of 
argument for a summary refutation of false theories. 



CHAPTER V. TRUTH OF THE PREMISSES. 



Article I. Formal and Material Logic. 

114. The Form. We have seen what is required in the 
quality and quantity of the premisses, and in the exten- 
sion of middle and extremes, in order that a given 
conclusion may be taken as lawfully drawn from given 
premisses. If I say, 

Every stea^nhoat is a sunflower, 
Every sunflower is a violin, 
Therefore, Every steamboat is a violin, 

and suppose the premisses to be true, I have to accept 
the conclusion, inevitably, from the premisses. The 
conclusion is in perfect accord with all the laws of the 
syllogism. All that formal logic has shown us to be 
necessary in quality, quantity and extension has been 
— supposing the premisses true — strictly attended to. 
Yet every proposition in the strange argument is false. 
This leads us to speak of the matter of the premisses, 
as affecting the acceptance of the conclusion. We shall 
say something, therefore, on the truth of the premisses. 
It may be urged that the subject does not belong strictly 
to the /(?;''/«(^/ logic. The formal logic has to deal, strictly 
speaking, only with the form, or structure, of argument 
necessary to have a conclusion rightly drawn from pre- 
misses; — the matter, or truth, of the premisses being 



TRUTH OF THE PREMISSES. 69 

left out of consideration. And for this reason is it called 
formal logic. By this is it distinguished from material 
logic. 

115. The Matter. Material logic will teach us what 
care must be taken in the use of the various means we 
have of arriving at the truth, that is in the use of our 
various faculties ; and when we may cease examining, 
and rest reasonably secure in mind as to the truth or 
falsity of what is expressed in a proposition. So that, if 
we should meet with a syllogism such as the following, 

Every timepiece is made of brass, 
All brass is organic matter, 
Therefore, Every timepiece is made of organic matter, 

material logic would have to tell us how to use our 
faculties, — that is, how far to trust the various faculties 
— in our search for truth in the propositions. It is only 
when we have decided as to how far we are to admit 
the propositions that the work of formal logic begins. 
Nevertheless, we begin the study of philosophy with 
formal logic, because we have had so much practical 
experience in the use of our faculties, that we already 
hold securely that many propositions are true, many 
others false, and many, again, doubtful ; and we want, 
at once, a safe and systematic rule for arguing from the 
known to the unknown. Therefore we study formal 
logic first. 

However, we shall here make a short consideration 
upon the truth and falsity of the premisses, and upon 
the corresponding adhesion of mind which we can give 
to the conclusion. Yet we shall do this in such a way 
as not to touch the question of the means we have for 
arriving at the truth. 



70 THE LAWS OF THOUGHT. 

116. Value of the Conclusion. We cannot hold to the 
conclusion any more firmly than we hold to the prem- 
isses. Supposing the form of the syllogism to be correct, 
if we are certain of the truth of the major and minor, 
we may be certain of the conclusion. If we have a 
lingering doubt as to the truth of either major or minor, 
that doubt will cling to the conclusion. If either major or 
minor be false, the conclusion is false ; and the argument 
is called a sophism or a fallacy. Sophism or fallacy is 
in the matter, not in the form. A defect in the form is 
called 2l paralogism. This has been abundantly treated 
in the preceding chapter (Nos. 80-102). 

When the major and minor are both truths of which 
we are certain, the argument is called a demonstratioji. 

Leaving aside the probable argument, we shall treat 
of the demojistratiou and of fallacies. 



Article II. The Demonstration. 
Direct — Indirect — Simple — Compound — A Priori — A Posteriori. 

117. Two Kinds. A demonstration is an argument in 
which the conclusion is drawn from premisses of whose 
truth we are certain. It may be direct or indirect ; and 
either kind may be a priori or a posteriori. 

118. Direct. In the direct demonstration we draw the 
conclusion we desire, directly from the premisses where 
we have compared its subject and its predicate with a 
middle term. Thus : 

Tixe soul can thinks 
flatter cannot think. 
Therefore, The soul is not matter. 



TRUTH OF THE PREMISSES. /I 

119. Indirect. In the indirect demonstration, instead 
of drawing our conclusion as coming directly from 
premisses in a syllogism, we show that the contradictory 
cannot be true, by exhibiting the absurd consequences 
that would follow from such contradictory. The indi- 
rect demonstration is of frequent use in geometry, 
where we show absurd consequences that would follow 
from not admitting the theorem laid down. 

120. Simple ; Compound. A demonstration is called 
simple when the whole argumentation is finished clearly 
and satisfactorily with a single syllogism. If, however, 
it be necessary to bring forward new syllogisms to prove 
the major or minor or both — which may not be clear, 
or may be called in question — and, perhaps, again, new 
sollogisms to prove the new majors or minors, the 
demonstration is called compound. All the longer theo- 
rems in geometry are illustrations in point. 

121. A Priori. An argument is called a priori when 
it advances from premisses which state truths that are 
prior in the nature of things to the truth stated in the 
conclusion. Thus we may advance from what we know 
about the nature of a cause or agent, to establish some 
conclusion regarding the nature of the effect it may 
produce. The name a priori is used, also, for an argu- 
ment where we advance from principles in their wider 
extension to an application of the same principles in a 
less wide extension ; as, for instance, from principles 
regarding the whole animal kingdom to conclusions 
respecting elephants and kangaroos. Likewise, when- 
ever we advance from principles to facts, as from the 
general truths about triangles to the exhibition of the 
truths applied in a particular given triangle. 



72 THE LAWS OF THOUGHT. 

122. A Posteriori. The a posteriori demonstration 
proceeds in the opposite direction. It advances from 
what is posterior in the nature of things to what is prior 
in the nature of things. From the existence of an effect 
it concludes to the existence of a cause ; from the nature 
of an effect to the nature of the cause. It rises from a 
given fact to the principle that must explain the fact. 
We have an illustrious example of the a posteriori argu- 
ment in the discovery of the planet Neptune. After a 
quarter of a century of observations made upon the 
planet Uranus, discovered by Sir W. Herschel, it was 
found that its movement did not correspond with the 
known forces of gravity acting upon it, especially from 
Jupiter and Saturn. There was a fact : movement. 
The movement must have a cause. The cause must 
be a heavenly body. The movement was of such a 
character, said Leverrier, that if it came from a single 
heavenly body, that body, at a given time would be 
found in a given point of the heavens. The telescope 
is directed, at the given time, to the given point; and 
there is found the planet Neptune ! 



Article III. Induction. 

Complete and Incomplete Induction — Example — Analogy. 

123. Deduction and Induction. We add here a special 
article about a peculiar kind of a posteriori argument, 
which, by custom, has been allowed to appropriate, as 
it were, the name Induction. Every a posteriori argu- 
ment is, indeed, an induction, as opposed to the a priori 
argument, which is a deduction. Deduction means the 



TRUTH OF THE PREMISSES. 73 

drawing out of a particular proposition or conclusion 
from the universal premiss. Induction, on the contrary, 
is a leading back to the universal from the particular. 
Every process of thought from the particular to the 
universal is inductive. We wish to speak of induction, 
in the usual and limited acceptation of the word, as 
signifying an argument which passes from a uniform 
experience of several individual cases to a universal 
conclusion covering them all. The induction may be, 
as it is termed, complete or incomplete. 

124. Complete Induction. The induction is called 
complete when after having really made an examination 
of all the cases of which there is question, and having 
found that the same proposition, varying only the sub- 
ject, is applicable to each case individually, we draw a 
conclusion in which we include them all in a single 
universal proposition. If, for instance, I, an American, 
step into a railway car and finding there five men. A, 
B, C, D, E, I discover gradually that A is an Ameri- 
can, that B is an American, that each of the five is 
an American, and conclude that all the men in the 
car are Americans, I go through the process of a 
complete induction. The complete induction is the 
exact reverse of a detailed deduction, in which, from the 
universal, that all the men in the car are Americans, I 
would conclude : A is an American, B is, C is, D is, E 
is, I am an American. 

We may sometimes think we have a complete induc- 
tion when, in reality, we have not. We are liable to 
overlook particular cases. Moreover, sometimes even 
when the greatest care is taken in the observation of 
facts in certain branches of the natural sciences, when 



74 THE LAWS OF THOUGHT. 

all the known facts have been classified under a general 
proposition, some new discovery will show that the 
general proposition is untrue, and that the induction was 
not as complete as it was believed to be. 

125. Incomplete Induction. It is to the inco^nplete in- 
duction, which bears the name in the strictest sense, that 
we wish to call particular attention. It is a process by 
which, from experience of a limited number of cases, we 
pass on to formulate a universal law. Thus we formu- 
late the laws of gravitation, of equilibrium, of reflection, 
of refraction, from a very limited number of cases ; and 
we hold these laws to be applicable, as universal propo- 
sitions, to cases tried and untried. Is the process law- 
ful .? 

We inquire more particularly into the matter because 
some modern logicians, of the school of experimentalists, 
make the study of induction the chief business of logic. 
The process of thought m.ay be accepted as lawful, — the 
experiments having been rightly conducted, — but, upon 
one condition. The condition is, that we admit the 
reality of such a thing as cause. This very condition, 
which is absolutely necessary to the validity of the process 
of induction, is not accepted by the great champion of 
induction among the experimentalists, Mr. J. Stuart Mill. 
The process, then, is lawful if we admit true causality; 
namely, that whatever begins to be, depends for its exist- 
ence upon some real influence exercised by something 
else in bringing it about. In other words, Every effect 
demands a cause. 

Recognizing this, we may set to work with experiment 
and observation at the process of induction. If we find, 
by repeated test, that the same consequent follows the 



TRUTH OF THE PREMISSES. 75 

same antecedent constantly and uniformly in whatsoever 
circumstances or adjuncts of time, place, quality or rela- 
tion the antecedent may be tried, and in all the variations 
of circumstances by composition, opposition, etc. ; if we 
find, on the other hand, that, suppressing the one ante- 
cedent in question, whilst leaving all the circumstances 
and adjuncts the same, the said consequent does not 
make its appearance in any of the cases when the ante- 
cedent is so suppressed ; if, again, varying the antece- 
dent, in the various cases, in quantity, intensity, direction, 
etc., we find that the consequent varies proportionally in 
quantity, intensity, direction, etc. ; in other words, if we 
find that said consequent follows said antecedent only, 
but always, and in regular proportion, — we are bound to 
recognize as really existing in said antecedent a certain 
power whereby it brings into existence the said conse- 
quent ; and, also, in said consequent, a certain real 
dependence for its existence upon the antecedent. We 
perceive the two to be related as cause and effect. But 
yet more. We perceive that the antecedent is cause by 
reason of something inherent to its very nature ; for we 
have made our observations, tests, experiments, abstract- 
ing from it everything but its essential, inherent nature. 
But the essential, inherent nature of that thing must be 
■present always where that thing is ; the same yesterday, 
to-day, to-morrow. Hence we conclude that the same 
thing will produce the same effect to-morrow as to-day. 
We formulate a universal law which reaches to the 
future. Mr. J. Stuart Mill has, of all writers, written 
best upon the manner of making the tests for an induc- 
tion. But as he does not recognize the reality of cause, 
as he puts no real connection hetwetn fore o-oin^ zxi^ fol- 
lowing, his conclusion is universal only to the extent of 



^6 THE LAWS OF THOUGHT. 

the tests actually made. What he builds up with one 
hand he tears down with the other. 

126. Example. Allied to induction is what is some- 
times called the argument from example. It concludes 
to the universal from a few cases ; and, even, it may be, 
from a single case, without the tests and observations 
prescribed for induction. Its value is rather in discovery 
than in proof. A superior, well trained and vigilant 
mind will often suspect, and even detect, the universal 
law in a single case ; but it will be necessary to go 
through the various tests, to make the law acceptable to 
the ordinary intelligence. In general use it is an argu- 
ment weak in point of logic. Logically, it suggests at 
most the possibility of a case. It is resorted to in ora- 
torical discussion. The orator has the advantage of 
forcing his listeners on without giving them time to 
examine, and urges them to act under the impression of 
a possibility. 

127. Analogy. The argument from analogy is still 
less reliable, logically, than the argument from example. 
It is a pure figure of rhetoric, a parallel between two 
cases of quite different orders. It is useful to persuade 
an audience that cannot listen to dry argument, but can 
listen very well to a story, and then follow out the appli- 
cation of the story, in all its details, to the question 
under treatment. 

128. Caution. In philosophical argument be wary in 
the use of example and analogy. It is so easy to give 
illustrations and to make comparisons. Therefore have 
we so many self-styled " scientists," to-day, setting them- 
selves up as professional discoverers, and flying to con- 
clusions which the slow, careful processes of induction 
do not warrant. 



TRUTH OF THE PREMISSES. JJ 

Article IV. Fallacies. 

Begging the Question — Evading the Question — Accident — A Dicto 
Simpliciter, etc. — Consequent — Cause — Question — Reference — 
Objections. 

129. Fallacy. We have distinguished the Fallacy or 
Sophism from the Paralogism. The paralogism is an 
argument with a flaw in the form. A conclusion, true 
in itself, may be found in a syllogism which is faulty in 
the form. The conclusion may be true, indeed, but it 
has not been proved. We have previously considered 
arguments, with regard to the correctness of the form 
(Laws of the Syllogism). This article has reference to 
the matter of the conclusion. Any argument with a 
false conclusion is a fallacy. The word, however, is 
applied, in its special sense, to falsely concluding argu- 
ments which have so much the appearance of correct- 
ness as easily to deceive the unwary or to silence those 
whose limited knowledge or intelligence does not enable 
them to detect the deceit. We shall not consider any 
fallacy which is an evident violation of the laws of the 
syllogism. Every equivocation is such, since it uses a 
word in two senses, and thus gives us four terms in the 
syllogism. We subjoin some fallacies arising from the 
matter. 

130. Petitio Principii or Begging the Question. This is 
to insert cleverly and covertly into the premisses the 
very thing that has to be proved. This is a favorite 
fallacy of demagogues haranguing listeners whose hearts 
are already in the conclusion. Communistic gatherings 
echo with arguments like this : 



78 THE LAWS OF THOUGHT. 

"All men are born into the world, equal, with equal 
rights to live, equally, upon the earth and to enjoy an 
equal share of the spontaneous productions of the earth. 
So that by Nature herself are they justified in asserting 
their equality against all comers. 

" But all the existing laws of society are in open con- 
flict with the equal rights of men and are framed only 
to increase the inequality. 

" Therefore, as we cannot get the rights of our equal- 
ity from society, we are by Nature herself justified in 
overturning governments and helping ourselves." 

Here, you see, the right to plunder is assumed covertly 
in order to justify plunder. 

The circulns vitiosus {vicioiLS circle) is of the same 
order as Xh^ petitio prmcipii. We prove, for instance, the 
fall of the apple from the tree by gravitation ; and, later 
on, we establish gravitation by the fall of the apple. 

131. Evading the ftuestion {ignorantia elenchi). Under 
this head may be ranged all those tricks of argument by 
which one tries to make the best of his case without 
offering proof; or to shirk an objection without showing 
it to be invalid. This may be done by assuming for 
proof or disproof something similar or analogous to the 
point in question ; or by attacking an opponent on the 
ground that he is not to be regarded as an authority on 
the subject {argumentmn ad hominem), thus arousing 
prejudice against his argument ; or by appealing to the 
passions of the reader or listener ; or by trying to shame 
an opponent out of the debate by citing against him 
authorities that have the respect of the listeners. 

This is an utterly illogical way of proceeding, but it 
may be followed with great effect. 



TRUTH OF THE PREMISSES. 79 

132. Fallacy of the Accident. This consists in assum- 
ing as essential what is purely accidental. Thus a man 
might argue against Christianity because some who pro- 
fess it are not exemplary in their conduct. However, 
evil-doers are never such by reason of Christianity ; they 
may be, in spite of it. 

133. A Dicto Simpliciter ad Dictum Secundum Quid, and 

vice versa. This is the fallacy of arguing from an un- 
qiialified statement to the same statement qualified, or vice 
versa. This fallacy pervades daily conversation. From 
the unqualified statement that a man is learned the 
popular mind jumps to the conclusion that he is learned 
in particular matters to which, perhaps, he has never 
given any attention. How many a man truly "learned" 
has had to pay for his name as "learned" by being 
consulted as though he were an encyclopaedia.'' This 
fallacy works with equal success in the opposite direc- 
tion. An exhibition of some knowledge in a few partic- 
ular matters is soon made the basis for the conclusion 
that the exhibitor is "learned." 

134. Fallacy of the Consequent. This consists in a 
misuse of the conditional syllogism. Thus some one 
says : If the gale is strong to-night, the toiver ivill fall. 
In the morning the tower is found to have fallen. The 
fallacy infers that the gale was strong. The truth is 
that the tower may have fallen under other agencies. 

135. Fallacy of the Cause. This lies in assuming as the 
cause of something that which is merely an accompany- 
ing or preceding circumstance, or at most an occasion. 
Thus we sometimes read in the newspapers that the 
political principles of a party in power are the cause of 
all the fluctuations in trade. Therefore, to secure steady 



80 THE LAWS OF THOUGHT. 

business, the administration must be changed. And 
when the administration is changed, and the same diffi- 
culties occur, the responsibility is shifted to the opposite, 
principles of the new party in power. Or we read that 
the cause of a bank robbery was the insecure system of 
bolts put on by a certain safe company, thus shifting the 
responsibility from the want of vigilance on the part of 
the authorities, and from that education of the head 
without the education of the heart, so prolific in evil- 
doers. 

136. Fallacy of the Question. This consists in asking 
a number of questions all of which are evidently to be 
answered in the same way, by yes or no ; and then very 
deftly inserting one question whose answer should be 
the opposite, but which is made to pass along with the 
others, as answerable in the same way. Thus the com- 
munistic orator: "Are we poltroons.'' Shall we reject 
the equality nature has bestowed upon us .'' Shall we 
see the products of the earth, which nature intended for 
all, piled up for the use of a few } Can we, as nature's 
freemen, refuse to vindicate our equality .'' Is there 
anything to prevent us from destroying } They refuse 
us a share in their millions. Shall we refuse them a 
share in our poverty .'' etc. Therefore, etc." 

137. Fallacy of Reference. This is untruth — the 
inventing of false references for the support of a propo- 
sition. People do not usually verify references, and 
hence may be easily deceived by a long array of author- 
ities [.''] cited at the foot of the page. 

138. Fallacy of Objections. This consists in pouring 
forth a volume of objections, one immediately after 



TRUTH OF THE PREMISSES. 8 1 

another before giving opportunity for reply. The adver- 
sary's time may be more than taken up in trying to 
answer one of them. Even then his long, careful answer 
may not be as effective with the audience (or reader) as 
the terse, captious objection ; and besides, the other 
objections will be carried away unanswered. 



CHAPTER VI. METHOD. 



Article I. Scientific Method. 

139. Scientific Method. Supposing the premisses to be 
true and the form of correct argumentation to be fully- 
understood and rigorously applied, there are still differ- 
ent methods which may be followed in the search for 
conclusions, in the pursuit of truth. Moreover, methods 
which may have proved most satisfactory to our own 
minds in the search for, and discovery of truth, we may 
find less satisfactory for communicating the same truth 
fully, briefly, and clearly to others. 

We do not refer here to the mere variations of order 
in which a number of truths, such as dates of events in 
history, may be learned or communicated, one after 
another. But we refer to methods of arriving at the 
knowledge of even one truth as a conclusion, i.e. in such 
a way as to possess, together with the truth, also the 
reasons for it. We speak of scientific methods which 
give us scientific knowledge. Science. 

140. Analysis and Synthesis. There are two kinds of 
scientific method, the analytic and the synthetic. The 
analytic proceeds by way of analysis or taking apart ; 
the synthetic, by way of synthesis or putting together. 
To take a broad example : the chemist analyzes, when 
he proceeds to find out the nature and proportions of the 

82 



METHOD, ^3 

various elements in a lump of crude matter brought him 
from the mines ; he synthetizes, when he puts together 
various chemical elements for the purpose of discovering 
some new law of combinations. Thus analysis proceeds 
from the whole to the parts ; synthesis, from the parts 
to the whole. 

Before considering the methods of synthesis and 
analysis we shall touch upon two other points, — defini- 
tion and division^ — the understanding of which will 
enable us to speak more briefly and more clearly about 
the methods. 



Article II. Definition. 

Nominal — Real — Descriptive — Genetic — Essential — Physical — 
Metaphysical — Rules. 

141. Definition. Correct definition is a thing always 
to be prized in writing and discourse, even for its effec- 
tiveness in concentrating vague thought and shortening 
discussion. A universal habit of correct definition would 
be fatal to false argument and would put an end to 
much debate that is carried on to tiresome lengths. But 
the habit of correct definition belongs to the trained 
master mind. And as most minds are not such, and 
as most men shirk the search and labor demanded by 
correct definition, therefore have we so much, in phi- 
losophy as in other things, that is written all around a 
subject instead of about it. But here we are called upon 
to give a definition of a definition. Therefore : A defini- 
tion is the expression in zvords of the meaning attached to 
a term ; or, a definition is the expression in zvords of the 
nature of an object. That is to say, there are two kinds 



'84 THE LAWS OF THOUGHT. 

of definition. If we fix our attention on the word, to 
make it known in its character as a sign, we have the 
nominal definition. If we fix our attention on the thing, 
to define what it is, we have the real definition. 

142. Nominal Definition. We give a nominal definition, 
(i) When we make known the sense in which we are 
using a term for the case in question ; (2) When we 
make known the meaning usually and generally given 
to a term ; (3) When we declare the true literal mean- 
ing of a term according to its derivation. Thus, infinite, 
from the Latin in (a negative particle) and finis (a 
limit), means zvitJiout limit. 

143. Ileal Definition. This may also be threefold, — 
descriptive, genetic, essential. 

The descriptive definition is nothing more than a 
description. It does not enter into the essence of the 
object. It gives such a combination of accidental fea- 
tures, circumstances, etc., as may suffice to make the 
object recognizable. Its treatment belongs to works on 
composition and style. 

The genetic definition (from genesis, origin) gives the 
process by which a thing is produced. A genetic 
definition of a circle would be : A plane surface gene- 
rated by revolving a straight line about one of its extremi- 
ties fixed. 

The essential definition names the essential parts of 
an object ; that is, those without which the object can 
neither be nor be thought of. According to the way 
in which we look at an object, we may find it made up 
of separable essential parts which, taken together, will 
•give us the whole essence; or of inseparable essential 
parts which, considered as taken together, will also give 



METHOD. 85 

US the whole essence. Such separable parts are called 
physical parts, and the enumeration of them is the 
real essential physical definition. Such non-separable 
parts are called metaphysical parts, and the enumeration 
of them is the real essential metaphysical definition. 
Thus, in man, spiritual soul and organic body are essen- 
tial parts ; they embrace all that is essential ; they are 
actually separable; taken together, they give us the 
essence. Hence to say that man is a being co)nposed of 
a spiritual soul and an organic body, is to give an essen- 
tial physical definition of man. Again, in man, animal 
nature and rational nature are essential parts ; they 
embrace all that is essential; taken together, they give 
us the entire essence. But they are not physically, that 
is actually, separable. Take away rational nature, and 
you have not animal nature left, but only a dead body ; 
for the principle of life is gone. Such parts are sepa- 
rable only in the consideration of the mind ; that is, in an 
order of things outside the real physical order, — or, in 
the metaphysical order. They are called metaphysical 
parts. Hence to say that man is a rational animal, is 
to give the essential metaphysical definition of man. 
This is the true definition in logic. It classifies accord- 
ing to those logical considerations spoken of in Chapter 
H., Article H. It gives the species by combining the 
two essentials of proximate genus and final difference; 
and there is no mistaking a thing thus defined. — It is 
the perfect definition. 

144. Eules for Definition. We may summarize the 
requisites of a good definition : 

I. The terms of the definition should convey a more 
definite idea than the single term expressing the thing 



86 THE LAWS OF THOUGHT. 

defined. This does not mean that every term in the 
definition should always be at once better known by 
everybody than the single term. When we define a 
circle to be a plane stirface luith a single ciwvcd line for 
a boundary every point of iv hick is equally distant from one 
fixed point in the surface, our definition is less intelli- 
gible to an ignorant person than is the term circle. But 
one who learns the meaning of the terms in the defini- 
tion will get from it a more definite idea than he had 
before possessing the definition of a circle. 

2. Make the definition such that it may be convert- 
ible by simple conversion (No. 76) with the term express- 
ing the object defined. Thus: if a circle is a plane 
surface . . . etc., then a plane surface . . . etc. (as above) 
is a circle. 

3. Do not define by a negation, by saying what a 
thing is not. However, sometimes a negative term 
comes up for definition. In this case separate it into its 
negative and positive parts, and define the positive part. 
For instance, injustice is the absence of justice. Now 
^Q.'ax\.Q, justice, and you shall have defined injustice. 

4. Use words in their exact literal meaning ; and 
when there is a choice of words, use such as are most 
commonly understood. 

5. In philosophical matters insist upon the essential 
metaphysical definition. It may sometimes be useful 
to begin with or to work upon the physical definition ; 
but never lose sight of the metaphysical. 



METHOD. 87 

Article III. Division. 

145. Scientific Division. Definition, the perfect logical 
definition, regards the comprehension of a term (Chapter 
III., Article V.). Division, the perfect logical division, 
regards the extension. This difference we must exam- 
ine into as being of serious importance in all scientific 
study. A few words, however, first, upon division in 
general and on certain divisions which are precisely 
the inverse of the essential definition whether physical 
or metaphysical. 

146. Parts, Physical and Metaphysical. We saw that 
essential definition (No. 143) is the enumeration of the 
essential parts, as taken together to form the zvJwle. 
Division, in general, is a separation of zuJiatever may be 
regarded as a ivJiole, a unit, into its parts. If we regard 
an essence as a whole, a unit, made up of the parts 
enumerated in the essential physical definition, we have 
what is called a physical whole, which is divisible by 
physical, actual division into physical parts. Thus man, 
considered as a physical whole, is divisible actually into 
the physical parts, spiritual soul and organic body. If, 
however, we regard an essence as a whole, a unit, made 
up of the parts enumerated in the essential metaphysical 
definition, we have what is called a metapJiysical whole, 
which is divisible by metaphysical, mental division into 
metaphysical parts. Thus 7nan, considered as a meta- 
physical whole, is divisible into the metaphysical parts, 
animal nature and rational nature. 

147. Actual Union. The union of parts in both cases 
is an actual union. The physical parts, however, are 
really separable ; the metaphysical parts, only mentally. 



88 THE LAWS OF THOUGHT. 

148. Integral Parts. Parts which are really separable 
but which are not essential, i.e. not absolutely necessary 
for the existence of the whole, though belonging to its 
integrity or entirety, are called integral parts. A hand 
or a foot is an integral part of man. 

To summarize, therefore : A whole, regarded in its 
essence as made up of real parts actually existing, may 
be considered as made up of physical parts, really sepa- 
rable ; or of metaphysical parts not really separable. 

Physical parts which, though belonging to the normal 
state of the whole, to its integrity, yet can be separated 
without destroying the essence, are called integral. 
Thus : a hand or a foot in man. 

149. Logical Division. To return now to logical divis- 
ion : the parts we are especially concerned with, in this 
article, and which we are to get at by logical division, 
are not such as are bound together in actual union by 
an actual bond of unity, so as to make a real, actual 
something. We are concerned with another kind of 
parts, those, namely, which are embraced by, and go to 
make up the extension of an idea or term, not those 
which are found in comprehension. We said that the 
perfect definition was the enumeration of notions con- 
tained in the comprehension. The perfect division is 
the enumeration of, the partitioning off of what can be 
reached by the extension of a term. This logical divis- 
ion is therefore the enumeration, the dividing up, of 
species under genus, or of individuals under species. 
A genus is a logical whole ; the species under it and 
their subdivisions are logical parts. A species is a 
logical whole ; the individuals it extends to are logical 
parts. 



METHOD. 



89 



The following diagram will explain better than words 
the precise distinction between logical definition and 
logical division. To define animal, we go upwards, 

Substance 

A 
Material 

Organic 

A 
Sentient 

A 



ANIMAL = 



■pefinition 




Rational (Man). 

I 



Irrational. 



I Charles, Frederic, Augustus, Hannibal, Scipio, etc. | | Vertebrata, Articulata, MoUusca, Radiata. 

I \ ^,_J ^ 



taking in the various notions in the comprehension : 
sentient, organic, material, substance. To divide animal, 
we go downwards, classifying all that can be reached by 
the extension of the term. 

150. Potential Parts. Every term taken in the reflex 
universal sense (Nos. 21, 23) expresses a whole which is 
divisible by this kind of division into the parts of its 
extension. As thus divisible it is called a potential 
whole, because it extends not only to what really exists, 
but also to what exists only in potcntia; that is, to what- 
ever of the same kind may exist. All the birds in the 
universe might be destroyed, still bird would express a 
potential whole embracing all birds past and all birds 
possible in the present and the future though they shall 
not all exist, — embracing them all as potential parts 



90 THE LAWS OF THOUGHT. 

into which it {bird^ is capable of being divided by logi- 
cal division. 

151. Logical Whole. This kind of whole, then, is the 
logical whole ; because, being the object of a reflex uni- 
versal idea, it does not exist as a unit in reality, but 
only by consideration of the mind. Thus man, consid- 
ered as the object (Nos. 21, 23) of the reflex universal 
idea, is not a one something that can actually be torn 
asunder into separate men ; nor can substance, taken as 
the object of a reflex universal idea, be really split up 
into material and immaterial substance. Yet in the 
mysterious process of thought, man, substance, do logi- 
cally embrace all men, all substances, actual and 
possible. 

152. Importance of Division. It is the logical division 
which we must be careful to have special regard for, in 
philosophizing. Philosophy deals with the universal. 
It is from beginning to end a combination and correla- 
tion of the comprehension and extension of ideas. The 
advantage of correct logical division in the study of a 
subject is evident. It maps out the whole question 
before us, at the start ; and saves us from time-losing, 
wandering discussions, as well as from incomplete treat- 
ment of the matter in hand. 

153. How to Divide. To divide correctly : 

1. Let the sum of the parts be exactly equal to the 
whole. 

2. Therefore see that no single member of the divis- 
ion is equal to the whole. A bad division of plants 
would be into those that grow and those that bear fruit. 
The first member is equal to the whole. 



METHOD. 91 

3. Do not make one member to include another or 
part of another. This would happen if substance were 
divided into inunatcrial, material, living and organic. 
Living enters into material and immaterial. Organic 
enters into living and material. 

4. Divide first into proximate and immediate mem- 
bers, and then, if possible, subdivide. The meaning of 
this is that we should first seek the widest general 
grand divisions and then see if we cannot regard these 
as new wholes to be subdivided, etc. 

5. In scientific matters prefer the logical division. 
See if the whole may not be regarded as a genus. 
Mark off the species. See, again, if any species, thus 
found, may be regarded, in its turn, as a genus (Chapter 
II., Article III.) ; and do not go on to divide into indi- 
viduals until a species cannot be regarded as a new 
genus. (See Diagram No. 30). 



Article IV. Analysis and Synthesis. 

154. The Question Put. We may now go on to the 

explanation of the methods referred to above (Nos. 139, 
140). A proposition is presented to us in study, reflec- 
tion, reading, conversation, debate. Is it true or false .-* 
We make an assertion. We do not doubt the truth of 
our proposition, but how shall we proceed to place it in 
evidence, by means of demonstration .'' An adversary 
advances a false statement. How shall we prove it to 
be false } A single object of thought is offered us for 
investigation. What propositions shall we formulate 
regarding it } What shall we predicate of it .-' Of what 
may it be predicated .■* 



92 THE LAWS OF THOUGHT. 

155. The Answer : Analysis and Synthesis. Our inves- 
tigation of any single object of thought must begin by- 
analysis or synthesis, and must advance by one or the 
other, either purely by analysis or purely by synthesis, 
or by changing about, as circumstances may prompt, 
from one to the other. Let the object of thought pre- 
sented for investigation be animal. We must begin by 
trying to make animal the subject or the predicate of a 
proposition. If we begin by making it a subject, we are 
using analysis ; we are beginning by the analytic method. 
If we begin by trying to use it as a predicate, we are 
using synthesis ; we are beginning by the synthetic 
method. Again, an entire proposition is presented to 
us : Animal is substance, or Animal is not mineral. We 
have to test the truth of the proposition. We must 
begin by studying the subject or the predicate. If we 
begin with the subject, we are using analysis ; if with 
the predicate, we are using synthesis. The meaning of 
all this and the reasons for the terminology will best be 
seen in the case of a complete proposition. 

156. Analysis. Take the propositions, Animal is sub- 
stance, Animal is not mineral. Are they true t We 
know that in an affirmative proposition the form (No. 
2o) of the predicate is included in the comprehension of 
the subject (No. 66) ; and that in the negative propo- 
sition the form of the predicate is excluded from the 
comprehension of the subject (No. 68). Suppose we 
begin by a study of the subject. To see whether the 
forms, substance, mineral, are comprehended in a?timal, 
we must take animal apart into all the forms implied in 
its comprehension. We must analyze it. We do this 
by taking it as a metaphysical ivhole, proceeding upward 



METHOD. 93 

(No. 149) from the metaphysical whole, rt'wm^/, through 
all the forms, parts, of its comprehension. There we 
find substance embraced in the comprehension, but not 
viiueral. Hence animal is substance, animal is not 
mi)icraL The process is nothing more than logical 
definition. 

157. Synthesis. On the contrary, if we begin by the 
study of the predicate, since we know that in an affir- 
mative proposition the predicate expresses some form 
that is contained in the comprehension of the subject, 
we shall — if the predicate be not merely the essential 
definition of the subject (No. 66) — we shall have to 
keep adding on to it what is compatible with it until we 
shall have gathered together all the forms embraced in 
the comprehension of the subject. Thus (No. 149) we 
keep on adding material, organic, sentient, one after 
another, to substatice, until we get a combination that 
gives us animal. This is synthesis. The process is that 
of logical division. In the case of a negative proposi- 
tion, — if it be true, — we may keep on adding to the 
predicate forever, and we shall never find a combination 
giving us the subject. This proves that the negative 
proposition is true. If in an affirmative proposition 
we fail to find the subject, this shows the proposition to 
be false. 

158. The Explanation Complete. These few words 
cover all the essentials of synthesis and analysis as sci- 
entific methods. The words analysis and synthesis are 
sometimes used in ways that are apt to confuse the 
mind. Reduce every mode of expression back to that 
of comprehension, remembering that it varies inversely 
with extension, and the confusion will disappear. 



94 THE LAWS OF THOUGHT. 

159. Singular to Universal, and Vice Versa. It is said 
that analysis proceeds from the singular, or particular, or 
less universal, to the more universal ; and that synthesis 
proceeds from the more universal to the less universal. 
This would seem to contradict all that we have been 
saying. But remember that reference is here made 
to the extension, which varies inversely, with the com- 
prehension. When we proceed from animal up to 
substance, we go from the less universal to the more 
universal in exteitsion, though from the wider to the less 
wide comprehension. Hence there is analysis in both 
cases. 

160. Complex to Simple, and Vice Versa. It is said that 
analysis goes from the complex to the simple ; synthesis, 
from the simple to the complex. Understand this of 
comprehension. This manner of expression is applied to 
the process from particular concrete facts to the universal 
law, for analysis; and to the process from the law to 
particular applications, for synthesis. But how is the 
single fact complex and the universal law simple .-' You 
will see it in an illustration. You argue from the par- 
ticular concrete facts regarding matter, to a universal 
law regarding matter. The single fact is complex. The 
matter you have is this or that kind of matter, organic, 
inorganic, vegetable, animal, mineral, gaseous, liquid, 
etc. You have a complex comprehension. You have 
to analyze the separate cases, and cut away from the 
comprehension, until you arrive at the simpler form, 
matter, simpler in comprehension, more universal in 
extension, to make your general law about all matter, 
without specifying this or that particular kind of matter. 

Induction is analytic. Deduction is synthetic. 



METHOD. 95 

161. Discovery and Instruction. The modern growing 
natural sciences groiv by analysis. The sciences that 
have been explored to satisfaction and present a com- 
plete whole, as also growing sciences, — botany, chemis- 
try, etc., — so far as they have been explored and classified, 
are best taught by the synthetic method. Analysis 
is best for discovery. Synthesis is, in general, more 
satisfactory for instruction. The two methods may be 
used alternately, in the same treatment of the same 
subject. A change is sometimes useful in the treatment 
to rouse attention. 

162. Analjrtic and Synthetic Sciences. A science is 
called analytic or synthetic from the method chiefly 
used in its development. If, however, both methods 
enter very largely on account of the nature of the 
subject-matter, we have the mixed method, properly so 
called. Logic and geometry are synthetic. The vari- 
ous branches that make up the modern physics are 
analytic. Civil engineering, taken as a whole, is mixed ; 
it implies the synthetic mathematics and also the result 
of analytic observation on material to be used, as well as 
climatic conditions, etc. — In this little book we have 
mingled analysis whenever it seemed useful for clear- 
ness or interest. 

163. Advice. With what has been said, the student 
will be enabled to follow up the complete working of 
synthesis and analysis by attention to the processes 
pursued in standard treatises on the various sciences. 

If you find yourself confronted with the burden of 
proof or investigation, observe the following : 

1. Work cautiously. 

2. Consult your actual knowledge. The general out- 



96 THE LAWS OF THOUGHT. 

line of your actual knowledge may determine your 
method. Particulars may be so scanty that you will see 
your way to lie only through general principles, by syn- 
thesis. Or facts may be in such abundance that you 
may set to work at once by analysis. 

3. Beware of being unconsciously betrayed into a 
fallacy. 

4. Be on the alert for the moment when you can 
formulate a definition of terms. 

5. In distributing and classifying, keep in view the 
logical division. 

6. When you have found something by analysis, go 
over it again by synthesis. This will map it out in your 
memory. 



Article V. Science. 

164. Science. With a clear understanding of what is 
required for correct thought, and with some insight into 
methods of procedure, we may go in pursuit of knowl- 
edge. Every perception of any truth is knowledge. If 
this perception be through a demonstration, it is called 
scientific knowledge. The perception, through demon- 
stration, of a complete body of related truths regarding 
a given object, is called science. 

165. Object of a Science. The same object may be 
the object of more than one science. For we may con- 
sider the same object under different aspects; and 
obtain, regarding it, different sets-of-connected-truths — 
each set complete without the other. In other words, 
we may consider different forms, or formalities, found 
in the totality of the comprehension of the object. 



METHOD. 97 

166. Material and Formal Object. The object, taken 
in the totahty of its comprehension, is called the mate- 
rial object of a science. The particular formality consid- 
ered, or this formality as affecting the material object — 
abstraction made from all the other formalities compre- 
hended — is called the fonnal object of the science. The 
whole corporeal universe is the material object v.gr. of 
both astronomy and chemistry. But the formal object 
of the science of astronomy is the mass, magnitude, 
distance, co-ordinated motions, etc., of the various masses 
of matter, called heavenly bodies, which make up the 
corporeal universe ; whilst the formal object of chemis- 
try is the substantial distinction between elements of 
matter and their respective capacities for substantial 
union with one another. Again, various things, even of 
different orders, may be united into one science by 
reason of a formality running through them all. Thus, 
spirit, matter, substance, accident, all contain in their 
comprehension, the formality of beitig ; and can be 
taken all together as the material object of the science 
of being. They can all be considered in the same 
science, under the aspect of being, and this will give us 
the science of Ontology. 

167. A Delusion. Knowledge acquired by scientific 
processes is scientific knowledge. The possession of 
such knowledge is the possession of science. No other 
knowledge has a right to the name. Children in pri- 
mary schools who are obliged to memorize a few facts 
about rocks or animals or flowers, are often instructed 
to a false acceptation of the word by being told that 
they are " studying science " ! ! Thus they come to 
regard geology, zoology, botany, any and every science, 
as merely a list of facts, and the acquisition of a science 
to be an affair of memory and not of reason. 













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EXPLANATION OF OUTLINE. 99 

In the preceding table or "Outline of the Sciences" we have advanced from 
the term of least comprehension and greatest extension, namely, the term, Being. 
That which is represented by the term or concept Being supplies the subject- 
matter for Ontology, the Science of Being. 

We go on trying to increase the comprehension and diminish the extension 
by adding the terms, Finite and Infinite, to Being. The division is not one 
of genus into species, as we have seen when speaking of analogy (Nos. 28, 36), 
yet it serves us for this very broad outline. Infinite Being is the subject-matter 
of the science called, in philosophy, Natural Theology. 

Continuing with Finite Being, increasing comprehension and diminishing ex- 
tension, we have, in a perfect division, Substantial Finite Being and Acciden- 
tal Finite Being. Ontology extends thus far, defining the notions of Infinite 
and Finite, and treating of Substance and of all that is not Substance, that is of 
Accident; quantity, quality, action, time, space, etc. It is general philosophy. 

Again dividing, and increasing comprehension, we have Material Substan- 
tial Finite Being and Spiritual Substantial Finite Being. We do not treat 
of bodiless spirit under the Finite, in philosophy. But taking the Material, in the 
wide sense of the term, we have the subject-matter of the science, Cosmology. 

Increasing the comprehension, again, by adding ANIMATE and Inanimate, we 
get in the Animate Material, etc., the subject-matter of the science, Biology, as 
general science of life. If we take the other subdivision. Inanimate M.-\tekial, 
etc., we find that range of sciences which treat of inanimate, inorganic matter : 
Physics, etc. 

We leave the Inanimate; and we divide the Animate, by adding to the com- 
prehension, into the Rational and the Irrational. The Irrational divided by 
adding to comprehension, gives us Sensitive and Non-Sensitive (the brute 
and the plant), with the sciences. Sensation, etc.. Vegetation, etc. 

Returning to RATIONAL Animate, etc., we find here the science of Man 
in general, or Anthropology. From this point forward we are engaged 
solely with Man. We can no longer divide into species. W^e use such divisions 
as will give us a complete and clear view of the subject, Man. 

By actual physical essential division (No. 146) we can divide MAN into 
Soul and Animal Body. The Animal Body, for general principles, we refer 
over to Sensation. Soul is the subject-matter of the Science, Psychology. 
Psychology will treat of the Nature of the Soul and the Fo'cvers of the Soul. 
The Powers of the Soul, we group under three headings : Fozuer of actuating 
sense-perception, etc. ; Intellect ; Free- Will. 

Intellect, we consider in its A'ature ; its Method of Work; its Supply of 
Material. The Method of Work constitutes the object (or subject-matter) of 
the .Science, Formal Logic. The Supply of Material for true thought gives 
us the object of the Science, Material Logic 

Under the heading of Free Will we treat of the Existence a7id Nature of Free 
Will; of the Norma or Rule of the Free Act; and oi Practical Morality. 77ie 
Existence and Nature of Free Will, we may readily refer to the treatise on the 
Powers of the Soul. In this way, accepting Free Will from Psychology, we have, 
left, the A^orma of Free Act and Practical Morality. These last two, Norma and 
Practice, taken together, form the subject-matter of the Science, Ethics. 

This is one presentation of the philosophical and subsidiary sciences. In study- 
ing, we begin upon the lowest line with Formal Logic. Next, we take up Material 
Logic. Thus equipped, we go back to Ontology, and follow do^n through the 
Finite until we reach the border line of Ethics. Here, we turn back to take up 
the study of Natural Theology, which we had omitted and for which we are now 
prepared. At length, with what philosophy can teach us of God and man and of 
the wide universe about us, we study, in Ethics, the practical conclusions to be 
drawn from the whole, to guide the actions of the free, intelligent being, Man. 

< 



POINTS FOR PRACTICE. — The practical utility of Formal 
Logic, and the mental training to be derived from it, depend alto- 
gether upon the skill acquired in readily discerning the comprehen- 
sion and extension of terms. The Laws of the Syllogism — Definition, 
Division, Synthesis, and Analysis — are all to be learned by the care- 
ful study of Extension and Comprehension. Special attention should 
be given to these two correlated points. Original illustrations should 
be sought for as a proof that those in the book have been understood. 

(9) Name objects of the simple apprehension or of the idea. (10) Give 
examples of judgments. (11) Upon what two principles does the mind 
work in reasoning? (13-15) What is a term, a proposition, a syllogism? 
(17-19) Give three classifications of ideas. (19) Examples of singular, 
particular, collective, universal ideas. (20) How are universal ideas classi- 
fied? What is meant by form, formality, or determination, in reference to 
ideas? (21-27) Examples of species, genus, difference, property, accident. 

(29) Name some forms that may be used both as generic and specific. 

(30) Give illustrations of highest genus, lowest species, subaltern genera. 
Tables of contents in scientific works will furnish examples. (32) Exam- 
ples of real and logical terms. (33-35) Univocal and equivocal terms. 
(36) What is an analogous term ? and why is the question of analogy 
introduced here? (37) Examples of the material, logical, real supposition 
of terms. (40) Examples of propositions, pointing out the subject, copula, 
and predicate. (41) Examples showing the difference between the logical 
and the grammatical predicate. (42) Examples of simple. (43) Com- 
pound. (45, 46) Categorical, conditional. (47, 48) Conjunctive and dis- 
junctive propositions. Show how they are reducible to the conditional. 
(54, 55) Examples of a priori and a posteriori judgments. Show why the 
a priori are called necessary, absolute, metaphysical, analytical; and the 
a /cij^,?re'(7r2, contingent, hypothetical, physical, synthetical. (59-61) What 
is meant by the extension and comprehension of terms or ideas? (62-63) 
What does the extension of a proposition depend upon? Examples of the 
four extensions of propositions. (65-70) Explain the laws which declare 
the extension of the predicate in universal and particular propositions, 
both affirmative and negative. Name and illustrate the one exception for 
the universal affirmative. (73) State what is absolutely necessary that a 
proposition may have the force of a negation. (76) Examples of the 
conversion of propositions, retaining and changing quantity and quality. 
(78) Of opposition in quantity and quality. (84) Explain the difference 
between consequent and consequence. (86) Give the analysis of an 
(original) argument. (88) Explain the true, primary meaning of Middle 
Term. (92) What is meant by the Moods of the Syllogism? (94-102) Nine 
Laws of the Syllogism. Compose faulty arguments or syllogisms, and show 
how each law may be violated. (104-107) Examples of syllogisms. Show 
how the conjunctive and disjunctive are reduced to the conditional. 
(108-113) Examples of enthymeme, sorites, polysyllogism , epichirem, 
dilemma. (i 14-122) Difference between formal and material logic; 
between direct and indirect demonstration; between simple and com- 
pound; between the a priori and the a posteriori. (124) Example of 
complete induction. (125) What is required for the validity of the incom- 
plete induction? (129-138) Examples of various fallacies. (145) What 
is the essential distinction between logical definition and logical division? 
(146) What is meant by physical and metaphysical parts? (149-153) What 
is a logical whole? logical division? What are logical parts? 

100 



ALPHABETICAL INDEX. 



Numbers refer to Paragraphs. 



Abstract idea, 17. 

Accident, inseparable and separable, 
26, 27. 

fallacy of, 132. 
Accidental form, 27. 
Adequate idea, 18. 
A dicto simpliciter, fallacy, 133. 
Affirmative proposition, 72. 
Analogy, argument from, 127. 
Analogous terms, 33, 36. 
Analysis, 140, 155, 156. 

explanation of terminology in regard 
to, 159, 160. 

in discovery and instruction, 161. 
Antecedent in syllogism, 83. 
Apprehension, simple, 9. 

as an act, 9. 

as representative, 9. 
A prion demonstration, 117, 121. 

judgment, 55. 
A posteriori demonstration, 117, 122. 

judgment, 56. 
Argument, 11, 15, 80. 

analysis of, 86. 

basis of, II, 85. 

styles of, 81. 
Argumentation, 11. 
Axioms, for extension and compre- 
hension of terms, 58. 

for argument, 11, 85. 

Begging the question, 130. 
Being, predication of, 28, 36. 
science of, 166. 



Cause, fallacy of the, 135. 
Caution, 103. 
Clear idea, 18. 
Collective idea, 19. 
Collective proposition, 63. 
Complete idea, 18. 
Compound demonstration, 120. 
Comprehension and extension of 
terms, axiom regarding, 58. 

of idea and term, 60, 61. 

in analysis and synthesis, 156, 157. 
Comprehensive idea, 18. 
Concept, 9. 
Conclusion, 11, 86. 

value of, 116. 
Concrete idea, 17. 
Consequence, S4. 
Consequent, fallacy of, 134. 

in syllogism, 83. 
Conversion of propositions, 76. 



Declaration, 10. 
Deduction, 11, 123. 
Definition, 141. 
nominal, 142. 
real, descriptive, genetic, essential, 

physical, metaphysical, 143. 
logical, 143, 156. 
logical, diagram of, 149. 
logical and division, difference be- 
tween, 145. 
rules for, 144. 
Delusion, a, 167. 

loi 



102 



ALPHABETICAL INDEX. 



Demonstration, ii6. 

direct, 117, 118. 

indirect, 117, 119. 

simple and compound, 120. 

a priori and a posteriori, 117, 121, 
122. 
Determination or form, 20. 
Diagram of figures in syllogism, 89, 
90, 91. 

of genus, species, etc., 30. 

of logical definition and division, 149. 

of propositions, 79. 

of sciences, 168. 

of seventh law for syllogism, 100. 
Difference, specific, 25. 
Differential idea, 25. 
Dilemma, 81, 113. 
Direct demonstration, 117, 118. 

universal idea, 21. 
Discovery by analysis and synthesis, 

161. 
Distinct idea, 18. 
Division, 145. 

physical, metaphysical, mental, 146. 

logical, 150, 151, 156. 

logical, diagram of, 149. 

importance of, 152. 

rules for, 153. 

Elenchi, ignorantia, 131. 
Enthymeme, 81, 109. 
Epichirem, 81, 112. 
Equipollence of propositions, 77. 
Equivalence of propositions, 77. 
Equivocal terms, 33, 35. 
Example, argument from, 126. 
Extension of terms and ideas, 59, 61. 

of terms, axiom, 58. 

of predicate, 66, 71. 
Extremes, extreme major term, ex- 
treme minor term, 87, 88. 
Evading the question, 131. 

Fallacies, 130-138. 

Fallacy, 116, 129. 

Figures of syllogism, 88-91. 



Form (formality or determination), 
20. 

specific, 22. 

generic, 24. 

accidental, 27. 

v/hen both generic and specific, 29. 
Formal logic, 2, 114, 115. 

Genera, subaltern, 31. 
Generic, 24. 

idea, 24. 

and specific, the same form, 29. 
Genus, 24. 

highest, 31. 
Grammatical predicate, logical and, 
41. 

Herschel, Sir W., 122. 
Highest genus, 31. 

Idea, 9. 

characteristics of, 18. 

classifications of ideas, 17-19. 

comprehension of, 60, 61. 

differential, 25. 

extension of, 59, 61. 

generic, 24. 

object of universal reflex, 23. 

specific, 22. 
Ignorantia elenchi, 131. 
Indirect demonstration, 117, 119. 
Induction, 123. 

complete, 124. 

incomplete, 125. 
Inference, 11. 

Judgment, 10, 38. 

as an act, 10. 

as representative, 10. 

immediate, 51. 

mediate, 52. 

a priori, necessary, absolute, meta- 
physical, analytical, 55. 

a posteriori, contingent, hypotheti- 
cal, physical, synthetical, 56. 

synthetic a priori, 57. 



ALPHABETICAL INDEX. 



103 



Kant, 57. 

Knowledge, representative, 8. 

Laws of extension of predicate, 71. 

of syllogism, 93-102. 
Leverrier, 122. 
Logic, artificial, 4. 

as an art, 6. 

as a science, 5. 

formal, 2, 114, 115. 

material, 2, 114, 115. 

natural, 3. 

the name, i. 
Logical and grammatical predicate, 
41. 

supposition of terms, 37. 
Lowest species, 31. . 

Major extreme, 87, 88. 

premiss, 83, 88. 
Material logic, 2, 114, 115. 
Material supposition of terms, 37. 
Method, advice regarding, 163. 

analytic, 154-162. 

mi.\ed, 162. 

scientific, 139. 

synthetic, 154-162. 
Mill, J. Stuart, 125. 
Mind, three acts of, 7. 
Minor extreme, 87, 88. 

premiss, 83, 88. 
Moods of syllogism, 92. 

Negative particle, 73. 

proposition, 72. 
Notion, 9. 

Object of a science, 165, 166. 

material, 166. 

formal, 166. 
Objections, fallacy of, 138. 
Objective, identity, 10. 
Ontology, 166. 

Opposition of propositions, 78. 
Oral expression of thought, 12. 



Paralogism, ri6. 
Particular idea, 19. 

proposition, 63. 
Parts, physical, metaphysical, separa- 
ble, inseparable, integral, union 
of, 146-148. 

potential, 150. 
Petitio principii, 130. 
Polysyllogism, 81, iir. 
Predicables, heads of, 28. 
Predicate of a proposition, 40, 65. 

logical and grammatical, 41. 

laws of extension, 66-71. 
Premisses in syllogism, 83. 

major, 83. 

minor, 83. 
Principii petitio, 130. 
Property, 26. 
Proposition, 14, 39. 

simple, complex, 42 ; compound, 

43- 
possible varieties of, 44. 
categorical, 45. 

conditional or hypothetical, 46. 
conjunctive, 47. 
disjunctive, 48. 
extension of, singular, particular, 

collective, universal, 62. 63. 
use of name " particular," 64. 
extension of predicate in, 66-71. 
affirmative, negative, 72. 
quality and quantity of, 74. 
relations of, conversion, equivalence 

or equipollence, opposition, 75-78. 

Question, begging the, 130. 
fallacy of the, 136. 

Real supposition of terms, 37. 
Reasoning, 11, 80. 

as an act, as representative, two 
working principles, 11. 

process of, 53. 
Reference, fallacy of, 137. 
Reflex universal idea, 21. 

object of, 23. 



I04 



ALPHABETICAL INDEX. 



Science, 164. 

object of a, 165. 

material and formal object, 166. 
Simple apprehension, 9. 

demonstration, 120. 
Singular idea, 19. 

proposition, 63. 
Sophism, 116. 
Sorites, 81, no. 
Species, 22, 23. 
Specific, 22. 

difference, 25. 

idea, 22. 

and generic, the same form, 29. 
Subaltern genera, 31. 
Subject of a proposition, 40. 
Supposition of terms, real, material, 

logical, 37. 
Syllogism, 15, 81, 82. 

antecedent, major and minor prem- 
iss, consequent in, 83, 

consequence in, 84. 

figures of, 88-91. 

moods of, 92. 

laws of, 93-102. 

simple, compound, conditional, con- 
junctive, disjunctive, 104-107. 
Synthesis, 140, 155, 157. 



explanation of terminology in re- 
gard to, 159, 160. 
in discovery and instruction, 161. 
Synthetic a priori judgment, 57. 

Term, 13. 

classification and use, 32. 

univocal, equivocal, analogous, 33- 
36. 

comprehension and extension, 59- 
61. 

extreme, extreme major, extreme 
minor, middle, 87. 

supposition of, real, material, logi- 
cal, 37. 
Thought, form of, 2. 

material of, 2. 

oral expression of, 12. 

Universal idea, 19. 

idea, direct, 21. 

idea, reflex, 21. 

idea, reflex, object of, 23. 

proposition, 63. 
Univocal terms, 33, 34. 

Whole, logical, 151. 
metaphysical, 146, 156. 
physical, 146. 



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